Basically the European Catholics helped the Roman Orthodox when they got friendly enough and the Romans Desperately needed help with the Muslim Turks. Pope Urban II he argued that it was a Christian duty to help the Byzantines against the Muslims. He backed this up with a edict forbidding Christians waging war on Christians except on alternating weekdays, and with a rousing speech that was distributed and publicly read by the clergy throughout the Catholic area.
What was the Result? The Crusades, which lasted for roughly 2 centuries, and one of which ironically ended up administering the coup-de-grace on the Byzantine empire.
