  We use blackfold methods to analyse the properties of putative supergravity
solutions in M-theory that describe the backreaction of polarised anti-M2
branes (namely, M5 branes wrapping three-cycles with negative M2-brane charge)
in the Cvetic-Gibbons-Lu-Pope background of eleven-dimensional supergravity. At
zero temperature we recover the metastable state of Klebanov and Pufu directly
in supergravity. At finite temperature we uncover a previously unknown pattern
of mergers between fat or thin M5-brane states with the thermalised version of
the metastable state. At sufficiently small values of the anti-brane charge a
single fat-metastable merger follows the same pattern recently discovered for
polarised anti-D3-branes in the Klebanov-Strassler solution in type IIB
supergravity. We provide quantitative evidence that this merger is driven by
properties of the horizon geometry. For larger values of the anti-brane charge
the wrapped M5-brane solutions exhibit different patterns of finite-temperature
transitions that have no known counterpart in the anti-D3 system in
Klebanov-Strassler.
