* Russia's more assertive military worries some in West
* Diplomats puzzled by big rise in Russia forces spending
* Moscow probes NATO airspace, holds "aggressive" manoeuvres
* Putin says world is far from being peaceful and safe
By Peter Apps
LONDON, Nov 1 (Reuters) - When NATO forces start a major exercise in Latvia and Poland this weekend, they will be rehearsing how to oust an anonymous invading enemy from a fictional region.
For some, however, exercise "Steadfast Jazz" will test how the Western alliance could deploy rapid reaction forces to its eastern flank - which borders Russia.
A militarily resurgent and swiftly rearming Russia is alarming NATO states that lie close to its territory, chiefly the Baltic States. Other alliance members are simply baffled, wondering why Moscow feels the need to spend vast sums on meeting a threat from the West they say will never materialise.
NATO stresses that the wargames are not aimed at Russia directly, although some officials say part of their point is to reassure eastern member states at a time when Russia is probing NATO airspace with bombers, building warships and conducting ever more sophisticated exercises.
From Nov. 2-7, "Steadfast Jazz" will involve about 7,000 troops and other personnel including special forces, as well as tanks, aircraft and ships. Officially the NATO Response Force is designed to operate anywhere in the world.
But in the Baltic States, which once lived under the Soviet Union, the wargames are also a rehearsal for an unlikely but plausible scenario closer to home.
"Russia as a country in the last five years has been increasing its assertiveness in the Baltic," Latvian defence minister Artis Pabriks told Reuters. "'Steadfast Jazz' is important to us as these are the first exercises where we really train to defend our territory."
NATO's Supreme Allied Commander General Philip Breedlove said the exercise would show the alliance's ability to fight sophisticated wars and defend its territory. Russian monitors would be invited.
"We have to be prepared for more high end military operations," he said in September, adding that NATO's counter- insurgency experience from Afghanistan was no longer enough.
By "high end" Breedlove meant combatting any possible threat from a well-armed state, rather than relatively crudely-armed guerrillas as in the alliance's most recent operations.
Russia's "high end" capability, experts say, is improving fast and NATO is responding. Apart from "Steadfast Jazz", NATO training near Russia recently included the "Brilliant Arrow" fast jet exercise in August in central Norway.
Such activity could antagonise Russia further. President Vladimir Putin has long complained that the collapse of the Soviet Union allowed the West to expand too far into Russia's traditional sphere of influence - particularly the former Soviet Baltic states.
BOMBER FLIGHTS, NAVAL, GROUND MANOEUVRES
Moscow and Washington have worked together in recent months on removing Syria's chemical weapons, but strains are clear.
For Putin, a stronger military and more assertive foreign policy are central to Russian ambitions. "Ensuring Russia has a reliable military force is the priority of our state policy," he said earlier this year.
"Unfortunately, the present world is far from being peaceful and safe. Long obsolete conflicts are being joined by new, but no less difficult ones. Instability is growing in vast regions of the world."
Last year, Russia announced its defence budget would rise by about 25 percent, pushing spending above that of France and Britain. Moscow says it will spend $700 billion by 2020, hoping to equip at least 70 percent of 1 million active-duty personnel with modern weapons. That will include 2,300 new tanks, 1,200 new helicopters, 15 new surface ships and 28 submarines.
Nikolas Gvosdev, professor of national security studies at the U.S. Naval War College, said Russia wants to regain something of its Soviet-era standing in the world. "It is restoring its conventional capabilities to back up claims to great power status," he said.
In operations reminiscent of the Cold War, Russian bombers now periodically approach NATO airspace. In response, British fighters scrambled 29 times in 2010-12 while non-NATO Japan and even neutral Sweden have been on the receiving end of such missions.
Latvia says Russian military aircraft have come close to flying over its territory 37 times in 2013 alone, compared with perhaps once or twice a year five years ago. Naval activity has risen, including a task force sent to the Arctic in August.
"We've seen an increase in the frequency of Russian military activities and the substantial modernisation of their capability," General Charles H Jacoby, commander of the U.S. Northern Command, said earlier this year. "While we must strive for increased cooperation... we must continue to be prepared to demonstrate the intent and the capability to defend our interests."
Exercises on land have particularly worried neighbours. Among the largest was September's "Zapad-2013" manoeuvres in Belarus. The Kremlin described these as largely anti-terrorist in nature but foreign analysts said they appeared to revolve heavily around conventional war fighting.
CO-OPERATION HOPES, CONFRONTATION FEARS
Not everyone believes Moscow can achieve its ambitions. A slump in prices for oil and gas, a major source of revenue, could devastate its budget, and the economy is already slowing.
Within the military, bullying, morale problems and corruption remain rife. Islamist militancy in the Caucasus swallows up resources while some Russian strategists are more worried about China than the West.
Much of Russia's resources, from fresh water to minerals, are in sparsely populated parts of Siberia within relatively easy reach of the Chinese border, while Beijing's military budget is growing even faster than Moscow's.
"(There is) a growing fear that Russia's vast natural resources endowment... is vulnerable if the country lacks the means to protect it," said Gvosdev.
Budget problems mean most NATO states are cutting defence spending. The handful of Russia's neighbours that can afford to raise expenditure, however, are doing so. As early as 2007, Norway announced it would expand its military and move much of it to new bases nearer the increasingly contested Arctic.
Poland is also in the midst of its biggest ever increase in military spending, earmarking $43 billion over the next decade to buy Western systems. Sweden is buying patrol boats.
Western officials say their priority remains to work with Russia. NATO jets have also trained with Russian counterparts on counter-terrorism exercises, while NATO warships have visited Russian ports. This month's NATO-Russia summit in Brussels saw agreement on further co-operation.
In mainstream NATO thinking, Russian behaviour such as the "Zapad-2013" exercise is more puzzling than alarming, although eastern members cling to Article 5 of North Atlantic treaty - which obliges members to help any ally that comes under attack.
"The very aggressive posture during... Zapad caused much concern among the Baltic states for whom Article 5 really matters," said one senior Western official on condition of anonymity. "However, the considered view is that the government of Russia does not pose a threat."
Another NATO diplomat told Reuters he believed there was little doubt Moscow was preparing its military for potential conflicts with well-armed nations.
"That has a lot of us scratching our heads and thinking: why?" the diplomat said, adding that NATO states had made clear they had no ambitions to expand eastward. "Why in the world would you actually be arming yourself for a conflict with us? Isn't that all a monumental waste of resources?"