He started with Krylia Sovetov in the Russian Hockey League in 1990. He played for the national Soviet Union team in 1991. Moved to the United States in 1994 where he played for the Detroit Falcons ice hockey team. He also played with other hockey teams in the United States including Quad City Mallards, Michigan K-Wings, and San Antonio Dragons. Zvyagin played in the 2006 European Champions Cup and was noted for stopping 4 goals in one game. He plays in his father's favorite team the Moscow Dynamo as a goaltender and joined then in September 2009 to Vityaz Podolsk.
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