  We show that additive and asymptotically additive families of continuous
functions with respect to suspension flows are physically equivalent. In
particular, the equivalence result holds for hyperbolic flows and some classes
of expansive flows in general. Moreover, we show how this equivalence result
can be used to extend the nonadditive thermodynamic formalism and multifractal
analysis. In the second part of this work, we obtain a Liv\v{s}ic-like result
for nonadditive families of potentials and also address the H\"older and Bowen
regularity problem for the physical equivalence relations with respect to
hyperbolic symbolic flows.
