To what extent was the calling of the First Crusade a response to Alexios's plea for help?

The calling of the first crusade by Pope Urban II in 1095 at Clermont can be seen as a response to the many pleas sent by the Byzantine Emperor, Alexios Comnenus. This was after vast swathes of land had been taken by the nomadic Seljuk Turks in Asia Minor and this threatened the stability of the Byzantine Empire. Crusaders that subsequently participated retook these lands such as Antioch and Nicaea, yet wouldn't return them to the Greeks, showing that this perhaps was not their primary motive.The main reason for the calling of the Crusade was thus to further the aims, power and stability of the Papacy, helping to assert its authority over the Greek East, especially after the Schism of 1054. This was also a response to the Gregorian Reform Movement that was started by Urban's predecessor, Gregory VII, which consisted of emphasising Church supremacy and authority. This then influenced the decision at Clermont to call the Crusade. As can be seen, the answer to this question is complex, with many different factors.