Western airlines started flying over the USSR in the mid-80s. Iran has been a busy route for all airlines for many years. Diversion has never been a problem, except that the diverting aircraft may be guided to that state's preference, rather than the pilots' preference!
Early routeings over the USSR followed the railway lines, since that was an obvious source of electrical power for the mainly NDB navigation aids (VORs were few and far between) and communications were brief and deliberate - often a position report would be replied to in Russian and then immediately translated into English.Thankfully, time has meant progress in all areas!