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We develop the basics of a theory of almost isometries for spaces endowedwith a quasi-metric. The case of non-reversible Finsler (more specifically,Randers) metrics is of particular interest, and it is studied in more detail.The main motivation arises from General Relativity, and more specifically inspacetimes endowed with a timelike conformal field K, in which case\emph{conformal diffeomorphisms} correspond to almost isometries of the Fermatmetrics defined in the spatial part. A series of results on the topology andthe Lie group structure of conformal maps are discussed.

Almost isometries of non-reversible metrics with applications to stationary spacetimes