Sterling Bank’s deal to acquire the Seattle-area operations of Boston Private Bank & Trust Co. helps Sterling grow its commercial banking business in the Puget Sound region, which is one of three top markets Sterling is targeting for growth. Sterling already has about 20 branches in the Greater Puget Sound region. And with the Boston Private deal, Sterling is adding three more. Sterling CEO Greg Seibly said Boston Private has about $270 million in loans and about $190 million in deposits in the…