  Two ideals $I$ and $J$ are called transverse if $I \cap J = IJ$. We show that
the obstructions defined by Avramov for classes of (sequentially) transverse
ideals in regular local rings are always $0$. In particular, we compute an
explicit free resolution and Koszul homology for all such ideals. Moreover, we
construct an explicit trivial Massey operation on the associated Koszul complex
and hence (by Golod's construction) a minimal free resolution of the residue
field over the quotient defined by the product of transverse ideals. We
conclude with questions about the existence of associative multiplicative
structures on the minimal free resolution of the quotient defined by products
of transverse ideals.
