Crossing timescale expressed in Myr. It corresponds to the last crossing inside the HZ. Up to 6 Myr for the most perturbed systems but also with the lowest number of asteroids still present in the system within 10 Myr of integration time. For the other systems, the crossing timescale is much lower because their belt still contain a huge number of “alive” asteroids. Indeed, the dynamics of the system needs more time to empty the asteroid belt population.