But several counties in NC HAVE tried to pass breed bans.
This page may be of some help in your search.
I'm not sure what area of SE AZ you are currently living in, but you will find a number of differences that you need to consider when comparing the SE AZ area to Asheville.
1. Weather - it's way colder in Asheville
2. Cost of Living - it's way higher in Asheville (do look at those RE and income taxes)
3. You will still find a religious bent in Asheville that is not as prevalent (IMHO) as SE AZ