Oriented cobordism of oriented submanifolds

Definition

Suppose $M_{1}$ and $M_{2}$ are oriented submanifolds of an oriented manifold $N$ . An oriented cobordism from $M_{1}$ to $M_{2}$ is an oriented submanifold with boundary inside $P \times I$ , that gives a cobordism between $M_{1} \times {0}$ and $M_{2} \times {1}$ (and such that the orientations match on the boundary).