  We study the degeneration and the gluing of Kuranishi structures in
Gromov-Witten theory under a symplectic cut. This leads us to a degeneration
axiom and a gluing axiom for open Gromov-Witten invariants. They provide then a
route to the construction of virtual fundamental chains via specialization.
Comments on the equivalence of the degeneration formula of closed Gromov-Witten
invariants by Li-Ruan/Li versus Ionel-Parker are given in the Appendix.
