Dear categorists, A new preprint about higher dimensional transition systems which is the sequel of my previous work "Directed algebraic topology and higher dimensional transition system". The previous paper was accepted last June to the New York Journal of Mathematics but for unknown reasons, everything is blocked in this journal (no new publications since June 15th !!). So the first paper is still available only in my webpage and in ArXiv. I will resubmit it soon with this new one. Here is now the new preprint: Title: Towards a homotopy theory of higher dimensional transition systems Abstract: We proved in a previous work that Cattani-Sassone's higher dimensional transition systems can be interpreted as a small-orthogonality class of a topological locally finitely presentable category of weak higher dimensional transition systems. In this paper, we turn our attention to the full subcategory of weak higher dimensional transition systems which are unions of cubes. It is proved that not only this category is locally finitely presentable as well, but also that there exists a left proper combinatorial model structure such that two objects are weakly equivalent if and only if they have the same cubes up to the first Cattani-Sassone axiom. This model structure is obtained by Bousfield localizing a model structure which is left determined with respect to a class of maps strictly larger than the class of monomorphisms. We also prove that two weakly equivalent higher dimensional transition systems are bisimilar with a very general notion of bisimulation and that the higher dimensional transition systems corresponding to two process algebras are weakly equivalent if and only if they are isomorphic. The appendix contains a technical lemma about smallness of weak factorization systems in coreflective subcategories which can be of independent interest. This paper is a first step towards a homotopical interpretation of bisimulation for higher dimensional transition systems. URL: http://www.pps.jussieu.fr/~gaucher/ Best regards, pg. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]