 Handle-slide isolation of a cancelling pair

In the intermediate-index range, if an attaching sphere $A_1$ meets a belt sphere $B_1$ at exactly one transverse point, handle slides can remove the intersections of every other attaching sphere with $B_1$. The dual slides then remove the intersections of $A_1$ with the other belt spheres. Each move uses a band to the unique pivot sheet and a local isotopy removing the old and new intersections. If $m_{ji}=A_j\cdot B_i$ and $\delta =m_{11}=\pm 1$, the remaining incidence block is $m_{ji}-m_{j1}{m}_{1i}/\delta$, the Schur complement of the pivot. Extreme-index cases need separate hypotheses.