Sync phone to new iTunes library without erasing data.

My iPhone 6 (iOS 6.0.2) is currently synced to my old macbook air (latest operating system).

I have recently bought a macbook pro from apple and would like to know how to sync my phone to this computer without erasing all my data on my phone.

I am able to back it up but I am unable to transfer any music or videos onto my phone that I currently have on my macbook pro without erasing existing data on my phone and replacing it.

Currently my iPhone is set up with my old macbook air however if I need to change this in some way I don't mind. I only need my phone synced to my macbook pro library.

Thanks,

Max.