  Blow-analytic equivalence is a notion for real analytic function germs,
introduced by Tzee-Char Kuo in order to develop real analytic equisingularity
theory. In this paper we give complete characterisations of blow-analytic
equivalence in the two dimensional case: in terms of the real tree model for
the arrangement of real parts of Newton-Puiseux roots and their Puiseux pairs,
and in terms of minimal resolutions. These characterisations show that in the
two dimensional case the blow-analytic equivalence is a natural analogue of
topological equivalence of complex analytic function germs. Moreover, we show
that in the two-dimensional case the blow-analytic equivalence can be made
cascade, and hence satisfies several geometric properties. It preserves, for
instance, the contact orders of real analytic arcs.
  In the general $n$-dimensional case, we show that a singular real
modification satisfies the arc-lifting property.
