SOCHI, Russia — As North American neighbors, Canada and the United States generally enjoy a good relationship. But in women’s ice hockey, that friendship ends at the Zamboni door.

The U.S.-Canada rivalry might be the strongest in Olympic sports, men’s or women’s.

The two adversaries are by far the best in the world, so dominant in their sport that at the last Olympics, many observers worried about the future of women’s hockey if other nations did not step up their game. Countries such as Finland, Switzerland, Russia and Germany have improved, but for now, those teams appear to be little more than warm-ups.

On Wednesday, the powers face off in preliminary play of the Olympic hockey tournament. They bring a history of competition, respect and — recently — a pair of fist-slinging brawls.

“Once you get on the ice, there’s no friends on that team. You’re playing Canada,” said Anne Schleper, a defenseman for Team USA.

Canadian forward Jayna Hefford, who has four Olympic medals, offered a bit of a backhanded compliment to her opponents: “You want to play the best, and next to us, the Americans are it.”

Lou Vairo, coach of the 1984 U.S. men’s Olympic hockey team, called the clash one of the fiercest in hockey.

“It’s a very fierce rivalry,” he said. “Jeez, as far as I can remember, all of the deciding big games have basically been decided in overtime or shootouts. That’s how close it is. And I think it’s that close again this time.”

In many cases, the North American players are just bigger. At its opening game Saturday, Canada towered over its Swiss opponents. The Swiss have three players at least 5 feet 8 inches tall — Canada has 12.

The Swiss players were scrappy, darting among their opponents and slinging elbows, but Canada won 5-0.

Team USA, meanwhile, routed Switzerland 9-0 on Monday. (And the Swiss are among the most improved in recent years.)

That was after the United States took on rising star Finland in a weekend match that saw the Yanks score less than a minute into the game against Noora Raty, one of the world’s best goalies, eventually winning 3-1.

Raty held off Canada until deep into the third period Monday. The Finns lost 3-0.

Indeed, it is goalkeeping that has been the key to helping other nations begin to lift their play against the dominating North Americans, said Katey Stone, coach of the U.S. women’s team. A good goalie allows the defense to support offensive play and score goals, she said, rather than always teetering back on its heels.

Vairo thinks another team could rise up and shock the two North American hockey powers, much in the way the 1980 U.S. men’s team shocked the world at Lake Placid. He pointed to the Russians as potential spoilers.

“The Russian girls don’t have pressure on them, and if they can sneak in and win a gold medal, they will be heroines forever,” he said. “They scare me.”

The North American antagonism goes back to 1998 in Nagano, Japan; women’s ice hockey debuted as a medal event, and the U.S. won the gold. The Canadians did not like those results, and they have been atop the podium at every Winter Olympics since.

Over the past few months, the rivals have played a seven-game stretch of matches leading up to Sochi. Canada took the first three; then the U.S. won four in a row.

Two of those games saw tussles break out into full-fledged fights — common in men’s ice hockey but a rare sight in the women’s game. Schleper said that in both cases, the Americans were sticking up for their teammates, “which I think is appropriate.”

In the first brawl in October, the Americans — including Schleper — rushed in swinging after a teammate knocked down the Canadian goalie and was shoved into the boards in retaliation.

Another melee in December forced nearly every player on the ice into the teams’ respective penalty boxes.

Mark Johnson, who coached the USA team in the 2010 Olympics in Vancouver, said the women will not likely toss punches this Wednesday. There is too much at stake, he said, and they will not want to risk a penalty that allows the other team a power play.

“We have to stay disciplined during the whole game,” agreed Lauriane Rougeau, a defenseman for Canada.

Unlike in the men’s game, the women on both teams also feel a significant responsibility to serve as role models to girls in Canada, the United States and around the world.

The pressure is there. Monique Allain, a 48-year-old principal at an elementary school in New Brunswick who volunteers with Canadian hockey at the Olympics, grew up playing on boys’ teams. Now, she said, “we have role models who have pushed boundaries. They kept pushing and pushing and pushing.”

She likes what the women are teaching kids in her school.

“We definitely take that to heart,” said veteran USA goalie Jessie Vetter. “Being a confident girl, a confident woman is huge and something I hope they take away from seeing us play — maybe not the best role model with those last couple of games against Canada where we had fights, but still you can be physical and go at ’em and at the same time you leave it on the ice.”

Jim Afremow, a sports psychologist and author of “The Champion’s Mind,” has worked with Olympians and said that in Sochi, the players will have to underreact to anything they consider untoward.

“Rivals are kind of like your best friend and your worst enemy at the same time,” he said. Teams push each other to be their best, he said, but emotions can get out of hand.

The challenge is “to leave the past in the past.”

But that can be hard. The veterans on Team USA remember the 2010 Olympics in Vancouver, when they lost to Canada 2-0 in the gold medal match before a thicket of maple-leaf fans.

“It burns in your heart every single day,” said Meghan Duggan, a forward and USA team captain. “You remind yourself and your teammates that you don’t ever want to feel that way again.”

The teams know each other so well that come Wednesday, they will understand what to expect, Hefford said. “It comes down to executing.”

And this first showdown, of course, is not the most important one in this Winter Olympics. That game comes in just over a week, on Feb. 20, for the gold.