  We examine how the universality of two-nucleon interactions evolved using
similarity renormalization group (SRG) transformations correlates with T-matrix
equivalence, with the ultimate goal of gaining insight into universality for
three-nucleon forces. With sufficient running of the SRG flow equations, the
low-energy matrix elements of different realistic potentials evolve to a
universal form. Because these potentials are fit to low-energy data, they are
(approximately) phase equivalent only up to a certain energy, and we find
universality in evolved potentials up to the corresponding momentum. More
generally we find universality in local energy regions, reflecting a local
decoupling by the SRG. The further requirements for universality in evolved
potential matrix elements are explored using two simple alternative potentials.
We see evidence that in addition to predicting the same observables, common
long-range potentials (i.e., explicit pion physics) is required for
universality in the potential matrix elements after SRG flow. In agreement with
observations made previously for Vlowk evolution, regions of universal
potential matrix elements are restricted to where half-on-shell T-matrix
equivalence holds.
