In 1082 the “crisobolo” or "gold note" proclaimed the Venice's supremacy in the Adriatic Sea. So the Venice's submission to Byzantium was finished and the City can be considered a free State.
(
Nel 1082, il “crisobolo” o bolla aurea sanciva la supremazia del Dogato veneziano in Adriatico. La soggezione di Venezia a Bisanzio apparteneva al passato e la città poteva considerarsi libera.)
So I think that Venice could start the game like a Byzantine's Vassal and in 1082 it breaks its relationship and Vassallage with the Empire.
What do you think?!