Multiple Intra-City Trips, what's our best option for First Class travel?

I plan to travel by train following my arrival in Italy on 3 June, from Rome to Florence, then a couple of quick trips to Rome and back the 4th and 5th, then to Varenna (on Lake Como) then 6th, then to Pescara on the 10th, and finally back to Rome on the 13th. Will the Eurail Italy Pass cover me for all these trips?
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