  We present a microlocal criterion for the equivalence of iterated nearby
cycles along different flags of subspaces in a higher-dimensional base. The
result is motivated by its application to Hitchin systems in the context of
Betti geometric Langlands.
  I thank Claude Sabbah for bringing papers of Maisonobe and Kocherperger to my
attention. Among many interesting results, they include assertions implying the
main assertions of this paper. I will leave this paper on the arXiv as a
possibly useful additional reference.
