Project Management - Merging two companies into one and manage two culture

Scenario - each company works in the same industrial market. One company is a multinational corporation (MNC) 3x's larger than the second company. The larger company has its headquarters in the US, and the smaller has its headquarters in India. Prior to the decision to merge, these 2 companies were fierce competitors. You have been appointed as the Project Manager to manage the merger....and you work for the larger organization. How would you approach this rather daunting challenge - in this case, how would you begin to manage the two cutlures?