While the first crusaders were being besieged at Antioch, Alexius was moving to relieve them with his army. Deserters informed him the city was on the verge of surrender and the situation was hopeless, so he turned back to Constantinople. The crusaders somehow managed to break the siege, and felt betrayed by the emperor, thus finding it a convenient excuse to ignore their oaths about returning any land they conquered to the Byzantine Empire.
So, what if Alexius continued on, and relieved the besieged Crusaders at Antioch? What effects would this have? Would the crusade leaders still go back on their oaths, or would the land fall into Byzantine hands as promised?