Yes, the relations between the Byzantines and the Italian trading states, especially Venice and Genoa, would be particularly interesting. A strong Byzantine Empire would have greatly reduced their profits and their position as the trade-hub of Europe. Would they have fought wars against the Byzantines over this? Probably, and that in itself has repercussions.
Victory for the Italian states, likely backed by the Hapsburgs, would have destabilized the Empire, possibly resulting in some fragmentation and erosion from the west. Victory for the Byzantines would likely have changed the historical trade routes such that Constantinople likely would have become the gateway to the east, instead of Venice. What then happens to the Renaissance? Without the wealth and cultural influences of eastern trade in Italy, does the Renaissance begin in Constantinople? What implications does this have for Christianity? Could Catholicism have emerged stronger in the long run? Would Orthodoxy have split apart instead?
I agree that the Egyptian rulers would have tried this, but I question whether they had the strength to do so. The Ottomans were able to assert control over all of North Africa because of the huge military and naval might they commanded. The pre-Ottoman rulers of Egypt never had close to that kind of power at their disposal, nor did they have the wealth to fund the pirates and local warlords who kept the pressure up on the Christians. For example, the Barbarossa brothers would have been only a minor nuisance if they had not received massive funding and huge fleets from the Ottomans. I doubt Egypt alone could have generated the resources to mimic what the Ottomans did.Here I'm sure that if Egypt remained "in the game", her power and reach would have expanded westward -the ambition to form a western pan-muslim empire (as opposed to the eastern/Persian) would still exist. The ethnic/religious fault-line between the straights of gibraltar would certainly have still existed.
At the same time, Spain never seemed particularly interested in North Africa for its own sake. The place was very poor and the efforts spent there were largely to suppress the pirates, not to conquer for profit or religion. I would expect low-level piracy to have continued, but not on a level sufficient to draw the attention of Spain and the Italian states, as it did historically. They would have gone about their normal business, seeking trade and colonization in the Americas and Asia, as they did historically, with their political noses turned towards Europe instead of the Med.
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