When two cycles have a transversal intersection X_1 intersection X_2 = Y on a smooth manifold M, then Y is a cycle. Moreover, the homology class that Y represents depends only on the homology class of X_1 and X_2. The sign of Y is determined by the orientations on M, X_1, and X_2. For example, two curves can intersect in one point on a surface transversally, since dim X_1 + dim X_2 = 1 + 1 = 2 = dim M - 0. The curves can be deformed so that they intersect three times, but two of those intersections sum to zero since two intersect positively and one intersects negatively, i.e., with the manifold orientation of the curves being the reverse orientation of the ambient space.
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