If I get conflicts, I would try to do the merge locally, rather than via Bitbucket.
You will get a 3-way merge dialog and you choose manually what changes to merge and what not. But it's quite easy to screw it up (e.g. for 5D3 123 I'm tempted to export all patches, start a fresh branch, and re-apply them).
Nanomad and g3gg0 are experimenting with patch queues. For local changes, I use "hg pull --rebase", or manual patches.