Thanks for using Apple Support Communities.
For more information on this, take a look at:
Using iPhone, iPad, or iPod with multiple computers
To transfer, your device must be set to "Manually manage music," sometimes referred to as manual mode.
Best of luck,
how i can sync my phone with new iTunes and keep my apps and contacts ?
The iPhone is not a backup device. The right way to do this is to copy the iTunes library from your old computer to your new one. Or from the backup of your old computer to your new one. If you can't do that your options are somewhat limited, but explained in this User Tip: Syncing to a "New" Computer or replacing a "crashed" Hard Drive