  We describe the infinite interval exchange transformations obtained as a
composition of a finite interval exchange transformation and the von
Neumann-Kakutani map, called the rotated odometers. We show that with respect
to Lebesgue measure on the unit interval, every such transformation is
measurably isomorphic to the first return map of a rational parallel flow on a
translation surface of finite area with infinite genus and a finite number of
ends. We describe the dynamics of rotated odometers by means of
Bratteli-Vershik systems, and derive several of their topological and ergodic
properties. In particular, we show that every rotated odometer has a unique
minimal subsystem, and that there exist rotated odometers whose minimal
subsystem does not factor onto the dyadic odometer.
