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You should define the transition maps via the method transition map of charts and not as a differentiable map, i.e. replace

to_MH_from_BL = M.diff_map(MMH, {(BL, MH): ...})

by

to_MH_from_BL = BL.transition_map(MH, ...)

and then use

show(gMann.display(BL.restrict(MMH.intersection(MBL))))

instead of show(gMann.display(BL) since gMann is not defined on BL's domain, as said in the error message.