Dime BanCorp and Anchor Bancorp, the two biggest thrift companies in the New York area, said Wednesday they had agreed to merge in a $1.2 billion stock transaction.

The merged company, to be called Dime Bancorp, will be the country's fourth-largest publicly traded thrift, with about $20 billion of assetS. Dime would enhance its standing as the largest thrift on the East Coast, and would add muscle in its battle for market share against New York-area retail giants like Chemical Banking Corp. and Citicorp.

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