  Using pagoda flop transitions between smooth projective threefolds, a
relation is derived between the Euler numbers of moduli spaces of stable pairs
which are scheme-theoretically supported on a fixed singular space curve and
Euler numbers of Flag Hilbert schemes associated to a plane curve singularity.
When the space curve singularity is locally complete intersection, one obtains
a relation between the latter and Euler numbers of Hilbert schemes of the space
curve singularity. It is also shown that this relation yields explicit results
for a class of torus-invariant locally complete intersection singularities.
