  We develop the basics of a theory of almost isometries for spaces endowed
with 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 in
spacetimes endowed with a timelike conformal field K, in which case
\emph{conformal diffeomorphisms} correspond to almost isometries of the Fermat
metrics defined in the spatial part. A series of results on the topology and
the Lie group structure of conformal maps are discussed.
