The pairwise entanglement dynamics in a multipartite open system consisting of three entangled cavity photons locally coupled with independent N-mode reservoirs is studied via concurrence. The initial states of cavity photons are prepared in two types of W-like states while the corresponding reservoirs are prepared in the factorable vacuum state. The result shows that all the pairwise concurrences of the total system including cavities and reservoirs undergo qualitatively different dynamical behaviors. Among the two W-like states, only one could exhibit entanglement sudden death (ESD) leading the corresponding reservoirs to exhibit entanglement sudden birth. In addition, by taking the entanglement of the corresponding reservoirs into account, entanglement invariants are constructed for the W-like state that does not undergo ESD.