they all share infastructure somewhere in the series of tubes.

Very little of that infrastructure is shared. Even less now that the agreement between Rogers and BellMTS is being unwound.

Rogers, Bell, and Telus each have their own separate switching, RF network, transport and core networks. They do interconnect (otherwise you couldn't call a customer on the other network), but that is a very "thin" connection at the edge of the networks.

Sometimes they rent space for their antennas on someone else's tower, or rent fiberoptic transport but that is not really "sharing" any more than your landlord is "sharing" with you.

Source: happily retired from network operations/maintenance in one of the "big 3" phone companies.