On the pull request page, you can chose to "Close" a branch after it is merged.
Why would you want to close it rather than just delete it?
From what I can tell, close is just a bitbucket idea that hides the branch in the main list of pull-requests/branches, but it will still appear in regular git views/source tree lists of branches. Is there some idea of close that git itself knows about it (that I am unfamiliar with)?
Note we often merge branches into develop locally either in SourceTree (with GitFlow button) or using jgitflow-maven-plugin, which deletes the branch locally but not on origin (bitbucket) - although I wish those tools would.