  We prove the motivic version of the DT/PT-correspondence in \cite{PT} and the
motivic flop formula of the curve counting invariants in the derived category
of smooth Calabi-Yau threefold DM stacks. The main method we use is
Bridgeland's Hall algebra identities and the motivic integration map of
Bridgeland and Joyce from the motivic Hall algebra of the abelian category of
coherent sheaves on a Calabi-Yau threefold DM stack $Y$ to the motivic quantum
torus, which is a Poisson algebra homomorphism.
