Arizona does not require any permit to carry openly or concealed. As long as you are not a 'prohibited person' it is fine to carry. I've carried in Arizona, and it's funny being stopped by a cop and asked for ID. I wanted to see his reaction to I gave him a Mexican passport and a hunting license from Texas. He was very confused and tried to argue that those were not valid for carrying a firearm. I handed him a copy of federal and state laws showing that a non-immigrant alien can lawfully possess a firearm as long as they are in the country legally, have an Alien Registration Number, and a hunting permit issued by any state.