On a family of stably handle-slide trivial R-links

An R-link is an n-component link L in S^3 such that Dehn surgery on L yields #^nS1 \times S2. Adapting work of Gompf, Scharlemann and Thompson, Meier and Zupan produced a family of R-links L(p, q; c/d), where the pairs (p, q) and (c, d) are relatively prime and c is even. For most of link in this family, whether it is handle-slide trivial remains open. In this work, we show one subfamily, L(3, 2; 4/d), are stably handle-slide trivial for all d.