Byzantine Reconquest

Clarification: This is a translation of the alternative history Reconquista Bizantina, originally written by me in the wiki in spanish.

In OTL, the Byzantine Empire disappeared in 1453 with the Take of Constantinople by the ottoman-turkish army led by Mehmed II. This event has already warned, because the byzantine army was very weak, and the Byzantine Empire didn't had sufficient support to fight against the ottomans. But, what would happened if the europeans had support the byzantines?