I don't think you're actually using both AT&T and Sprint's towers. Sprint is a CDMA carrier while AT&T is a GSM carrier and the technologies aren't compatible with each other. If you bought the device through Straight Talk, then it's using Sprint's towers. If you brought your own device to Straight Talk, you're using either AT&T or T-Mobile. Since Verizon is a CDMA carrier, there's no way to transfer your service from Sprint's towers to Verizon's. ST sells a couple of phones that run on Verizon's towers, but the GS3 isn't one of them. They also allow you to bring your own Verizon 3G only phone and they can flash that and get it to work with them as well. However since the GS3 uses LTE, it is not compatible with that program.