The indirect-expansion solar assisted heat pump (SAHP) is one of the main configurations for SAHP systems. Previous work on this configuration has focused only on one-stage heat pump cycles using traditional refrigerants, which will be phased out in the future. In addition, one-stage heat pumps may not work properly in cold climate regions. To evaluate the performance and understand the potential of indirect-expansion SAHPs using CO2 as a refrigerant for space heating in cold climates, models of an indirect-expansion SAHP with a one-stage transcritical CO2 cycle, with a two-stage transcritical CO2 cycle, and with the presently popular one-stage R410a cycle for space heating in Toronto, Canada were developed using the combined platforms of EES and TRNSYS. Based on these models, the performance variations of the three systems with solar thermal collector area, storage tank volume, and heat pump compressor capacity were simulated, compared, and presented. The comparison of the systems showed that the performance of the two-stage cycle peaked at a much smaller compressor capacity than that of the other cycles - 0.4 m(3)/h for the two-stage cycle, 0.7 m(3)/h for the one-stage cycle, and 1.7 m(3)/h for the R410a cycle. When the three systems operated at the optimal compressor capacity, the free energy ratio (FER) of the two-stage cycle could reach 0.772, which was higher than that of the one-stage cycle by 19.0% and higher than that of the R410a cycle by 11.6% at the given conditions. The potential cost reduction benefits from the smaller compressor and higher FER could make the two-stage cycle more competitive than the other cycles in cold climates.