If someone is arrested in Minnesota based on an arrest warrant from another state, normally the person will be held for in-custody transport to the other state. In order to fight extradition, the defendant may sit in custody for weeks. Then, the circumstances under which extradition can be successfully fought to avoid transport are rare. The in-custody transport can be quite lengthy and uncomfortable; as well as somewhat costly for the prosecuting authority bringing the defendant back. If a person were arrested in Minnesota on an out of state warrant, the normal next step is for Minnesota to contact the jurisdiction issuing the warrant to ask whether they want the person held for transport. If the answer is no, the person is released. That could happen within a day, or within weeks.
A person released in that circumstance, may wish to contact a criminal lawyer in the state where the matter is pending. The lawyer can contact the prosecutor to inquire about resolving the case. In my experience, however, the defendant will have a stonger position if they are back in the state, get the warrant cleared, have a court date, prepared to fight the old case pretrial and at trial. The prosecutor may have problems with the old case, but might not disclose that in until shortly before a contested hearing or trial.
I agree with Mr. Gallagher. If AZ wants you, there is no way to resolve the matter without going to AZ. You have a right to an identity hearing before you are ordered to go to AZ. At an identity hearing, all they have to establish is that you are the person named in the warrant in AZ. Your good conduct over the last 7 years is important info in mitigation of sentence--if you reach that point in AZ--but it will not prevent your extradition.
Normally, you would have been charged as a fugitive from justice. This is a felony complaint filed against you by the county that arrested you on the warrant. You are held on the charge and a bail can be set. If you don't waive extradition, then the two states have to get the extradition paperwork together and a hearing is held to determine if you are the person they want back in AZ. If you waive extradition, AZ has 30-90 days to get you; otherwise, you can be released. This is a very general explanation of the process. It is really very complicated. It appears that none of this has occurred. I could be that AZ is not interested in coming to get you and will just wait and hope they arrest you if you ever return to AZ. If you truly want to resolve this forever, call an experienced criminal defense attorney practicing in the AZ county where you are charged and have the warrant. That attorney can speak to the prosecutor and attempt to make a deal that will resolve the warrant and ultimately the case. I have done this a couple times with AZ prosecutors with and without the assistance of local counsel. Good luck.