Equipment and Mark of Mutiny

If I were to gain control of a creature with equipment on it (via mark or threaten) can I then re-equip the equipment to one of my other creatures?

I was watching LSV draft, and he marked a sellsword with a grappling hook on it, equipped adventuring gear to it and swung. when the sellsword went back to the other guy so did the adventuring gear. I think that the proper play would have been to move the hook to his other guy and then swing with both. Sure his opponent would have a larger sellsword, but LSV would have kept his adventuring gear and stolen a grappling hook.

Not going to look this up in the official rules but when creatures exchange control the equipment and enchantment still belong to the owner.

The owner of the equipment still controls that equipment even if they lose control of the creature wearing it. They may unequip from the mc'd creature at the start of their main phase. Also any "may" abilities of that equipment are still at the discretion of it's owner.

For example if the equipment said "whenever equipped creature deals damage you may have target player lose 5 life"
the owner of the equipment could make his opponent lose 5 life if he attacked with the mc'd equipped creature.

ok so in the case of adventuring gear: player A equips adventuring gear to a creature. Player B takes control of that equipped creature. The Landfall ability of adventuring gear occurs when player A plays a land, regardless of whose control the equipped creature is under.