  We propose a refinement of the notion of blow-Nash equivalence between Nash
function germs, which is an analog in the Nash setting of the blow-analytic
equivalence defined by T.-C. Kuo. The new definition is more natural and
geometric. Moreover, this equivalence relation still does not admit moduli for
a Nash family of isolated singularities. Some previous invariants are no longer
invariants for this new relation, however, thanks to a Denef & Loeser formula
coming from motivic integration in a Nash setting, we managed to derive new
invariants for this equivalence relation.
