We address the question of the classification under blow-Nash equivalence of simple Nash function germs. We state that this classification coincides with the real analytic classification. We prove moreover that a simple germ can not be blow-Nash equivalent to a nonsimple one. The method is based on the computation of relevant coefficients of the real zeta functions associated to a Nash germ via motivic integration.
"Blow-Nash types of simple singularities." J. Math. Soc. Japan 60 (2) 445 - 470, April, 2008. https://doi.org/10.2969/jmsj/06020445