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In this work, Einstein's view of geometry as physical geometry is taken intoaccount in the analysis of diverse issues related to the notions of inertialmotion and inertial reference frame. Einstein's physical geometry enables anon-conventional view on Euclidean geometry (as the geometry associated toinertial motion and inertial reference frames) and on the uniform time. Also,by taking into account the implications of the view of geometry as a physicalgeometry, it is presented a critical reassessment of the so-called boostabilityassumption (implicit according to Einstein in the formulation of the theory)and also of 'alternative' derivations of the Lorentz transformations that donot take into account the so-called 'light postulate'. Finally it is addressedthe issue of the eventual conventionality of the one-way speed of light or,what is the same, the conventionality of simultaneity (within the same inertialreference frame). It turns out that it is possible to see the (possible)conventionality of distant simultaneity as a case of conventionality ofgeometry (in Einstein's reinterpretation of Poincar\'e's views). By taking intoaccount synchronization procedures that do not make reference to lightpropagation (which is necessary in the derivation of the Lorentztransformations without the 'light postulate'), it can be shown that thesynchronization of distant clocks does not need any conventional element. Thisimplies that the whole of chronogeometry (and because of this the physical partof the theory) does not have any conventional element in it, and it is aphysical chronogeometry.

Einstein's physical geometry at play: inertial motion, the boostability  assumption, the Lorentz transformations, and the so-called conventionality of  the one-way speed of light