A treatment of the twin paradox based on the assumption of an instantaneous acceleration

We investigate the twin paradox assuming the acceleration acts instantaneously on one of the twins and that its effect is just to revert the relative movement of the twins keeping the same relative speed. The relative motion of the twins is then split in two stages: one where they move away and another when they approach each other. Each stage is described by specific Lorentz transformations that obey certain boundary conditions related to the reversion of motion. We then show how the paradox arises from the particular form of the Lorentz transformation describing the approaching movement of the twins.