Doubly slice links, double branched covers and embeddings in S^4

A classical result states that the double branched cover of S^3 along a doubly slice link admits an embedding into the 4-sphere S^4. After clarifying the meaning of this statement, I will illustrate how this can be used to prove that certain Seifert manifolds, as well as other manifolds which arises as the boundaries of plumbed 4-manifolds, can be proved to have an embedding in S^4..