Classification of linking 2-spheres

Suppose there is a link K consisting of two disjoint embedded 2-spheres S12, S22 in R5. By the Hurewicz theorem and the Alexander duality, one obtains the isomorphism π2(R5 - S22)≅Z By fixing the orientations of S12 and S22, it fixs the sign of the above isomorphism and hence defines a fixed integer to S12 in π2(R5 - S22)≅Z. This number is called the linking number of K. Up to homotopy, this linking number obviously classifies the link. Following from a Zeeman's paper, "Isotopies and knots in manifolds", the linking number also classifies the link up to isotopy. Now adding an extra condition: S12, S22 have only one maximum and one mimimum when we project R5 → R1 to a fixed direction (such links is called a good links), and all isotopies keep to have one maximum and one minimum (such isotopies are callded good isotopies). This paper uses a different approach from Zeeman's by the extensive usage of Whitney move to classify the good link, up to good isotopy, by its linking number