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).