Before revision:  A noncrossing blocking pair of a matching M is a pair (m,w) of a man and a woman such that they are not matched with each other but prefer each other to their own partners in M, and the segment (m,w) does not cross any edge in M. A weakly stable noncrossing matching (WSNM) is a noncrossing matching that does not contain any noncrossing blocking pair.
After revision:  A noncrossing blocking pair of a matching M is a pair (m,w) of a man and a woman such that they are not matched with each other but prefer each other to their own partners in M, and the segment (m,w) does not cross any edge in M. A weakly stable noncrossing matching (WSNM) is a noncrossing matching that does not admit any noncrossing blocking pair.