  The key notion to understand the left determined Olschok model category of
star-shaped Cattani-Sassone transition systems is past-similarity. Two states
are past-similar if they have homotopic pasts. An object is fibrant if and only
if the set of transitions is closed under past-similarity. A map is a weak
equivalence if and only if it induces an isomorphism after the identification
of all past-similar states. The last part of this paper is a discussion about
the link between causality and homotopy.
