Hi Doug,
I'm a loooong time lurker here at TheHighRoad who has emerged from lurkerdom to respond to your question.
AZ is an "open carry" state, which means that as long as the weapon is legal to own and is visible, you can walk down the street with it on your person.
AZ is also a "shall issue" state. Our "permits" are referred to as CCWs (concealed carry weapons). If you obtain one of these cards with which the state acknowledges your right to carry any darn weapon any darned way you choose, you can then legally carry your weapon concealed. Our CCWs are not weapon specific -- it does not have to be a particular handgun that you qualified with. Furthermore, it doesn't even refer to a "firearm." Instead, it refers to "weapon." So you can also carry concealed a long-bladed knife or other legal weapon.