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Why didn't “Europe” support the byzantine empire against the turks?

Why didn't catholic Europe support the byzantine empire against the turks? Or did they? How? Yes, there were some indifferences between the catholic and ortodox interpretation of the bible but the turks were muslims and should have been considered much worse (c.f. the "reconquista", shouldn't they? They co-operated during the crusades and the European empires (franks, Habsburg) should have appreciated Byzantine as a buffer towards the muslim world?