If Akshan steals one of my equipments and then attaches it to another unit using Jax, when Akshan dies do I gain control of the equipment again?

Yes, when the Akshan that stole your equipment leaves the board, you regain control of that equipment.

According to the ruling in FAQ #694 and FAQ #5396, control-change effects are tied to the source that created them (in this case, the Akshan). When that source leaves play, the control-change effect stops applying.

Here is the sequence of events:

1. Akshan steals the equipment: Akshan's ability creates a control-change effect that grants the Akshan's controller control of your equipment.
2. Equipment is moved: Even if the equipment is moved to another unit (using an effect like Jax's ability), the control-change effect from the Akshan remains active. You do not control the equipment while the Akshan is in play.
3. Akshan leaves the board: The control-change effect stops applying.
4. Control returns: With no other control-change effects active, control of the equipment reverts to its original controller (you).

Important Nuances:

• Attachment: As noted in FAQ #694, the equipment does not automatically detach or return to your hand when Akshan leaves; it remains attached to its current unit until it is moved by a card effect or the unit it is attached to leaves the board.
• Control vs. Attachment: While you regain control of the equipment, you cannot use the equipment's own "Equip" ability while it is attached to a unit, because attached gear has inactive rules text (Rule 718.2). You would need to use an external effect (like Weaponmaster) to move it to one of your own units if you wish to use it.