  We find that quasiperiodicity-induced localization-delocalization transitions
in generic 1D systems are associated with hidden dualities that generalize the
well-known duality of the Aubry-Andr\'e model. For a given energy window, such
duality is locally defined near the transition and can be explicitly determined
by considering commensurate approximants. This relies on the construction of an
auxiliary 2D Fermi surface of the commensurate approximants as a function of
the phase-twisting boundary condition and of the phase-shifting real-space
structure. Considering widely different families of quasiperiodic 1D models, we
show that, around the critical point of the limiting quasiperiodic system, the
auxiliary Fermi surface of a high-enough-order approximant converges to a
universal form. This allows us to devise a highly-accurate method to compute
mobility edges and duality transformations for generic 1D quasiperiodic systems
through their commensurate approximants. To illustrate the power of this
approach, we consider several previously studied systems, including generalized
Aubry-Andr\'e models and coupled Moir\'e chains. Our findings bring a new
perspective to examine quasiperiodicity-induced localization-delocalization
transitions in 1D, provide a working criterion for the appearance of mobility
edges, and an explicit way to understanding the properties of eigenstates close
and at the transition.
