Near Santa Maria della Fava is another little neighbourhood church, San Lio; founded in the 9th-century as Santa Caterina, its dedication was changed after the canonisation of the Pope Leo IX (d. 1054) because he had taken Venice's side in a spat (atypical of any pope, actually; usually Venice and Rome were at complete loggerheads).
The church saw a famous miracle in 1474: there was a member of the Scuola di San Giovanni Evangelistra who didn't believe that the confraternity's relic was the real thing. When the reliquary was taken along to the doubter's funeral in San Lio, however, it became extremely heavy and could not be carried inside the church, which was taken as proof positive of its authenticity. The event is pictured in Giovanni Mansueti's Miracle of the Relic of the Holy Cross in Campo San Lio in the Accademia.
Image by Didier Descouens, Creative Commons License