  We establish several equivalent characterisations of the anchored
isoperimetric dimension of supercritical clusters in Bernoulli bond percolation
on transitive graphs. We deduce from these characterisations together with a
theorem of Duminil-Copin, Goswami, Raoufi, Severo, and Yadin that if $G$ is a
transient transitive graph then the infinite clusters of Bernoulli percolation
on $G$ are transient for $p$ sufficiently close to $1$. It remains open to
extend this result down to the critical probability. Along the way we establish
two new cluster repulsion inequalities that are of independent interest.
