  On a finite momentum grid with N integration points and weights the
Similarity Renormalization Group (SRG) with a given generator G unitarily
evolves an initial interaction with a cutoff on energy differences. This
steadily drives the starting Hamiltonian in momentum space to a diagonal form
in the infrared limit corresponding to a permutation of the eigenvalues and
depends on G. Levinson's theorem establishes a relation between phase-shifts
and the number of bound-states. We show that unitarily equivalent Hamiltonians
on the grid generate reaction matrices which are compatible with Levinson's
theorem but are phase-inequivalent along the SRG trajectory. An isospectral
definition of the phase-shift in terms of an energy-shift is possible but
requires in addition a proper ordering of states on a momentum grid in order to
fulfill Levinson's theorem. We show how the SRG with different generators G
induces different isospectral flows in the presence of bound-states, leading to
distinct orderings in the infrared limit. While the Wilson generator induces an
ascending ordering incompatible with Levinson's theorem, the Wegner generator
provides a much better ordering, although not the optimal one. We illustrate
the discussion with the nucleon-nucleon (NN) interaction in the 1S0 and 3S1
channels.
