The most commonly proposed plan to build a colony on Mars (notably the plan SpaceX is actively building) involves building a ship, launching it to space then have it (or part of it) land on Mars, then it stays there (part in orbit part on mars) until it's time to leave and flies back.
What I'm wondering is that what if instead there will be a spaceship between the two planets that never stops? each time it nears one it uses gravity assists to slingshot to the other planet, all cargo (astronauts, fuel, etc) is loaded via shuttle rendezvous in the time of the slingshot, same for disembarking.
While this have pros & cons the one I want to focus on is fuel economy, on one hand it saves the need to decelerate and accelerate to and out of orbit each time (and potentially get a gravity assist boost to help out each time too) but on the other the course will likely need more corrections as the ship never stops to wait to just the right time to begin the interplanetary part of the journey.
Will overall this save fuel? is it possible to roughly know how much (in percentage)?