Akshan, Mischievous

Q. If I take control of an equipment then move the equipment to another unit (say with Jax's ability for instance), what happens when Akshan dies?

The control of the stolen equipment is regained by the original controller, but the equipment remains attached to the unit until it dies or the gear is moved/detached by another ability.

718.5.e. Attached cards may have different Controllers from their Top-Most card.
718.5.f. Changes in Control of the Top-Most card do not impact Control of Attached cards and vice versa.
718.5.g. An Attached card still appends the abilities in its Effect Text to the Rules Text of the Top-Most card and modulates the Top-Most Card’s Might by its Might Bonus.