Duplicates on Playlist from Homesharing

I have recently moved my iTunes library to another computer. In order to get my playlists, I also copied them (seperately from the music). Now, if a song has appeared on a playlist or more than one, I have a multiple of it. However, my new iTunes library treats each file as seperate (that is, if it's on two playsits, there are three copies).

When I go to delete duplibcates, I am essentailly removing them from my playlists (which I don't want). How can I move both my library and playlists without ending up with duplicates. What's more, how can I fix my current iTunes library? Is there a way to consolidate the EXACT SAME song? Thanks in advance for any help.