Changing home network on SIM card
Afaik Verizon can only unlock the phone completely and not block certain carriers.

Until the iPhone 5, there was no model that supports CDMA and GSM.

The reason your phone doesn't work on an AT&amp;T network (or most international networks for that matter) is because AT&amp;T doesn't run a CDMA network.

http://support.apple.com/kb/ht3939