  Using analytical tools from linear response theory, we systematically assess
the accuracy of several microscopic derivations of Israel-Stewart hydrodynamics
near local equilibrium. This allows us to "rank" the different approaches in
decreasing order of accuracy as follows: Inverse Reynolds Dominance (IReD),
Denicol-Niemi-Moln\'ar-Rischke (DNMR), second-order gradient expansion, and
14-moment approximation. We find that IReD theory is far superior to
Navier-Stokes, being very accurate both in the asymptotic regime (i.e., for
slow processes) and in the transient regime (i.e., on timescales comparable to
the relaxation time). Also, the high accuracy of DNMR is confirmed, but
neglecting second-order terms in the Knudsen number, which would render the
equations parabolic, introduces serious systematic errors. Finally, in most
cases, the second-order gradient expansion (a.k.a. non-resummed BRSSS) is found
to be more inaccurate than Navier-Stokes in the transient regime. Overall, this
analysis shows that Israel-Stewart hydrodynamics is falsifiable, and the
relaxation time is observable, shedding new light on the debate on the
viability of transient hydrodynamics as a well-defined physical theory
distinguished from Navier-Stokes.
