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To add to what Miriam said, as I am in the process of handling a merger for a client right now and am dealing with this same issue. In my client's case, they are building a new website that represents the merged company, migrating the content from both sites into one (in many cases content on both sites is redundant so we eliminate/consolidate some) and then we will use 301 redirects mapped from the old site content to the new site content.