  Approximation of real analytic functions by Nash functions is a classical
topic in real geometry. In this paper, we focus on the Nash approximation of an
analytic desingularization of a Nash function germ obtained by a sequence of
blowings-up along smooth analytic centers. We apply the result to prove that
Nash function germs that are analytically equivalent after analytic
desingularizations are Nash equivalent after Nash desingularizations. Results
are based on a precise Euclidean description of a sequence of blowings-up
combined with N\'eron Desingularization.
