Sure, the New York Giants are facing the Buffalo Bills in the Super Bowl this week. But before you start singing "New York, New York," get a map of New Jersey - the Giants play there, in the swamps, west of the Big Apple.

But the Giants' stirring victory over the San Francisco 49ers has also stirred passions on either side of the Lincoln Tunnel, with folks on both side claiming the NFC champions as their own.No surprise there; we're talking about two states that went toe-to-toe over the Statue of Liberty, Staten Island garbage dumps, the Westway project, corporate raiding.

New York and New Jersey share the Hudson River and a hearty animosity, but little else.

"The Giants live in New Jersey, not New York. They play in New Jersey, not New York . . . And when the victory parade is held, it will be in New Jersey," read a pointed editorial Tuesday in the Newark (N.J.) Star-Ledger.

Not if New York Mayor David Dinkins has his way. Dinkins claimed the men in blue as the Big Apple's own and promised a celebration; East Rutherford, N.J., Mayor James Plosia said there was no question the Giants were Jersey guys.

New York Gov. Mario Cuomo - apparently not satisfied with the Buffalo Bills as the Empire State's representatives - called the Giants native New Yorkers.

"It's all New York. You can't lose. It's two born-in-New York teams," Cuomo crowed Monday, although 24 hours later he pledged his allegiance to the Bills.

Cuomo's first comment perplexed Garden State Gov. Jim Florio's spokeswoman Nancy Kearny, "A lot of people seem to be forgetting their geography. . . . The Giants play on this side of the Hudson."

Dinkins' stance is quite a change from the previous city administration. When the Giants won the Super Bowl in 1987, irascible Ed Koch let it be known the champions weren't welcome here and no ticker-tape celebration would be staged.

Thirty years ago, in the days of Gifford and Huff, there were no such geographic quandaries: The Giants played in the Bronx and owned Manhattan.

But times changed. The Giants went into a two-decade tailspin; they opted for a new stadium in Jersey. They moved into the Meadowlands in 1976, while retaining the New York prefix to their name.

So who do the Giants belong to? At least one fan says everybody.

"Hey, there's a lot of Giant fans in Connecticut. There's Giant fans all over the world," said Steve Kennedy, of Pompton Lakes, N.J.

"They play in New Jersey, but the corporate name is New York. I don't care what they're called. Besides," he concluded, "New Jersey gets all the revenue, right?"