To give you an idea of the handoff sequence, this is the sequence of an IFR flight from Red Deer last Saturday:
Coming in IFR to CYBW (Calgary, Springbank) from the west, north west or south west you will talk to: 1. Edmonton Centre (132.85) , 2. Calgary Terminal (west - 128.7), 3. CYBW outer tower (118.2), 4. CYBW inner tower (120.7), 5 ground (121.8.
Leaving CYBW IFR you will talk to Ground (for clearance), inner tower, Calgary Departures (124.52), Edmonton Centre.
Note the difference in nomenclature between "Calgary Terminal - west" and "Calgary Departures" as different ATC people/teams manage inbound and outbound flows. If you were to fly in to Calgary International (CYYC), instead of Terminal you might be handed off to talk to "Calgary Terminal East" (on 119.4) but would probably talk to Calgary Arrivals.
Finally, Calgary International has a separate clearance frequency if I recall correctly.