To analyze the violence among the Shias of Iraq one must answer one question. Is it better for the Shias of Iraq to cooperate with Iran, and support the Shia pipelines (Iran-Iraq-Syria), or is it better for them to cooperate with the Arabs and the Turks, and support the Sunni pipelines (Qatar-Turkey) and the Shia-Sunni pipelines (Shia Iraq – Sunni Iraq – Sunni Syria – Turkey)?
The Shia pipeline (Iran-Iraq-Syria) supposedly has Russia's support, but the truth is that Russia does not want any pipeline of the Middle East to reach Europe, because it would hurt the Russian exports to Europe. For Russia the Iran-Iraq-Syria pipeline is a necessary evil in order to block the Qatar- Turkey pipeline.
The Sunni pipeline (Qatar-Turkey) has the support of United States, or it used to have the support of United States, because now it is difficult to say whether the United States is closer to Iran or closer Turkey, due to the American-Turkish rivalry in Syria over the issue of ISIS and the Kurds. The Americans were supporting the Kurds against ISIS in Syria, and the Turks were supporting ISIS against the Kurds. Now we see the Turks changing their stance towards ISIS, and I guess that will ease a bit the relationship between Turkey and United States.
In the initial stages of the Arab Spring we saw the Shias of Iraq aligning themselves with Iran, which was a normal thing, given Iran has been traditionally supporting the Iraqi Shias against the Sunnis of Iraq. But now the Iraqi Shias are in power, and they need the Americans and the Iranians only as long as they have to fight the Sunnis of Iraq, who are supported by the Turks and the Arabs of the Gulf.
But if the Iraqi Shias were to normalize their relations with the Sunnis, and therefore the Turks and the Arabs would stop supporting the Sunnis of Iraq against the Shias of Iraq, the Iraqi Shias would no longer need the Iranians and the Americans. And then the Iraqi Shias could align themselves with Turkey, in order to send oil and natural gas to Turkey through the Sunni parts of Iraq and Syria, and enjoy Turkey's military protection. Remember that Shia Iraq is rich in oil, and therefore it is a natural competitor of Iran, while Turkey has no oil and gas, and therefore is a natural buyer of Iraqi oil and gas. That's the reason Turkey had relatively good relations with Saddam Hussein. They were also hunting the Kurds of Iraq and Turkey together.
Moreover the Iraqi Shias do not need Iran to access the Persian Gulf, because they already have access to the Persian Gulf. The whole idea of the Iraq-Iran alliance was that Iraq would allow to reach the Mediterranean Sea through Iraq, and in exchange Iran would allow Iraq to use the Mediterranean Sea through its influence in Syria. Other than that the two countries are natural competitors in the oil and gas markets. Therefore if the Shias of Iraq do not thing they have a chance of reaching the Mediterranean Sea, they would no longer have a motive to cooperate with Iran against the Sunnis. Instead they could use Turkey to reach Europe.
Obviously if the Iraqi Shias and the Turks reach an agreement, the Russians and the Iranians will use the Kurds of Turkey and Syria to block them. The Russians and the Iranians could also use the argument that Syria is a single country,