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The incumbent Republican, Charles Bass, was once the kind of Republican that fit New England perfectly and had a home in the national Republican Party. For 12 years, he was a leader in the shrinking ranks of moderate Republicans, an environmentally minded member and often a thorn in the side of Republican leaders. Then came 2006, and he was swept out along with almost every other Republican in the Northeast. The son of a former congressman and the grandson of a governor, Mr. Bass came back and reclaimed his West New Hampshire seat in the 2010 tidal wave, after Representative Paul Hodes, a Democrat, vacated it to run for the Senate. But the 3,550-vote win was not convincing. The loser in that race, Ann McLane Kuster, a lawyer, has been plotting a rematch ever since. Another scion of New Hampshire politics, she has raised more money than Mr. Bass, is something of a favorite of the political left, and may be a slight favorite in November.