Spreading religion with caravans
The pressure is towards your city.
Normally religion pressure is only exerted to a certain range around any particular city. Venice being a religion-founding holy city doesn't change that range. Trade routes bypass this range limit mechanic, and the cities will be considered in range once connected by a trade route. So presumably by this, Venice is out of range to pressure you normally, but setting up a caravan will allow their religion to spread your way.