The first important thing is that my own timeline doesn't start the war until the year 2000. But it doesn't really matter as the events that drew Turkey out of NATO and toward Iran could be transfered at an other time.
The starting point comes from January 1995. At the time it seems that the CIA managed to negociate a truce between various kurdish factions. Following this, an attempt at assassinating Saddam was to be conducted by Iraqi soldiers (using tanks) in relation to a military offensive by the Kurds (In this case, the Kurds would not have had to fight much of the Iraqi army). That action was not authorized and the ploters were arrested.
I chose to take another path and the action is, in fact, authorized. Benefiting from US backing the Kurds launch their attack and the Iraqi officers manage to kill Saddam by tank fire. Of course, as often with the CIA, things don't exactly turn as expected.
Following the assasination, Iraq enters a period of civil war where Shia are opposing the Sunni and the Kurds. The Shia put their hands on most equipements from regular Iraqi units but they lack proeficient military officers. Nevertheless, they slowly rebuild the army with help from Iran. In the middle of the civil war they establish the Islamic Republic of Iraq under the leadership of Al Sadr (the actual Al Sadr's father). The Kurds and the Sunni still benefit from US support and they are joined by most of the Republican Guard. As a result, their smaller manpower is balanced by superior skills and equipments. In the meantime, the Kurdish PKK still launches various attack on Turkey and keep seeking refuge in Kurdish held Iraq.
Finally, in 1997 running out of patience, Turkey launches a large scale offensive on the PKK which once again withdraw to Iraqi Kurdistan. Pushing further than it did before, Turkey enters Iraq on several occasions. US, refusing to support Ankara, asks for a UN resolution condemning Turkey's military action. In the meantime, Iraqi Kurds provide several stingers to the PKK and several Turkish aircrafts are destroyed. The Turkish people feel betrayed and demonstrate against the USA, attacking the US embassy. Instead of moving against its people the Turkish Army, which suffered significant casualties at the hand of the Kurds, puts the Islamic leader back to power and forces a change of the constitution. Slowly Turkey moves toward a more radical Islam and annouces that it leaves NATO. According to the treaty, all NATO bases in Turkey will have to be closed within a year.
Of course, this is not enough to bring Iran and Turkey toward each other. The point is that Turkey finds itself isolated and looking for new allies. For Ankara, turning to Moscow remains unacceptable as several wounds from the past are still to be healed. However, soon before the events that led to Turkey leaving NATO, Ankara has created the Developing-eight (D-8 for short) an economic development alliance (Turkey, Bangladesh, Egypt, Iran, Indonesia, Malaysia, Nigeria and Pakistan) and turns to this for support. The new situation and the tensions with the USA push some members to resign (Egypt and Pakistan) but the others remain, one is eager to help (Iran) and several more join (Islamic Republic of Iraq, Lebanon, Syria...). At first, Iran gets mostly technological support from Turkey in return for financial support but a tighter alliance is under way and, when the Twilight War starts over Europe, the military collaboration quickly evolves into military alliance.
Basically that's it. As you see, I have developped my own Mediterranean Union but it si centered on Turkey. So many things could have go wrong between 1990-2000.
