More like: launch to earth orbit (dropping the first and second stages, that land at spaceports for shipping home and refuelling), dock to a larger ship (nuclea

More like: launch to earth orbit (dropping the first and second stages, that land at spaceports for shipping home and refuelling), dock to a larger ship (nuclear?) which carries them to Mars, un-dock in Mars orbit and make a powered descent to the colony there. And then do the whole thing again backwards.