  This paper analyzes commensurability of the class of surface automorphism
generated by two Dehn multitwists. We show pairwise noncommensurability between
several classes arising from canonical curve configurations. In addition, we
consider the Kenyon-Smillie invariant J of flat surfaces in this setting. We
also introduce a general construction of infinite classes of commensurable
pseudo-Anosov homeomorphisms.
