  We establish tight bi-Lipschitz bounds certifying quasi-universality
(universality up to a constant factor) for various distances between Reeb
graphs: the interleaving distance, the functional distortion distance, and the
functional contortion distance. The definition of the latter distance is a
novel contribution, and for the special case of contour trees we also prove
strict universality of this distance. Furthermore, we prove that for the
special case of merge trees the functional contortion distance coincides with
the interleaving distance, yielding universality of all four distances in this
case.
