Your 2001 Chevrolet Silverado uses "quick connect" fittings for the heater hose connections at the firewall. If they are damaged the complete hose must be replaced. If the pipes on the heater core are damaged then the heater core will need to be replaced also.
There are 2 one of them is the inlet and the other the outlet. the one withe the black fitting you will need to change the whole hose the white one you can buy the new fitting only at the dealership about 40 buck and you can replace that one but there is a tool you will need i just did this on my 2002 silverado 2500hd very easy