On almost blow-analytic equivalence

Abstract

We study the analytic equivalence of real analytic function germs after desingularization and state the cardinality of the classes under this equivalence relation. We consider also the Nash case, and compare these equivalences with the blow-analytic or blow-Nash equivalence. We prove an approximation result after desingularization: Nash function germs that are analytically equivalent after analytic desingularizations are Nash equivalent after Nash desingularizations.