I use Lab Corp for monthly INR testing. My local one keeps both my insurance info and the actual script from my Doctor - which is for 6 months - on file. However, this info is NOT available to other Lab Corp locations, which means you'll need to take a bunch of signed scripts with you.
PITA, really. If pharmacy chains like CVS and Walgreens will let me fill a prescription anywhere, why can't a lab chain like Lab Corp keep my info so it's available to all their locations?
Oh, and I looked into getting testing done in Canada, and the labs up there won't honor a script written by a US doctor, only ones written by a Canadian doctor. I still haven't decided how I'm going to deal with that when I take my long planned trip to Newfoundland.