  Two subset germs of Euclidean spaces are called blow-spherically equivalent,
if their spherical modifications are homeomorphic and the homeomorphism induces
homeomorphic tangent links. Blow-spherical equivalence is stronger than the
topological equivalence but weaker than the Lipschitz equivalence. We introduce
the thin-thick decomposition of an isolated singularity germ - which happens to
be a natural blow-spherical invariant. This decomposition is a generalization
of the thin-thick decomposition of normal complex surface singularity germs
introduced in [7]
