Allies getting equipment whose BLOOD (not pool) cost is reduced to zero

Hello!

Normally, equipment/loquipment that has a blood cost cannot be equipped by allies, per the rulebook:
"Only a vampire with enough blood on them can play a card with a blood cost."

If the card's blood cost has been reduced to zero (e.g. British Museum, Therbold Realty), is it still considered to have a blood cost? Is there a difference between "no blood cost" and "blood cost of zero," or are they equivalent terms as far as game mechanics are concerned?

QUESTION: "If British Museum is in play, can my ally take an action to equip The Catacombs from my hand?"

(Yes, we know that the ally can't USE the Catacombs, but we still might want to cycle the card this way. Also, British Museum + Therbold Realty + Pier 13 is a thing.)

Thanks much!
-Billy / Killiam


Name: The British Museum, London
Cardtype: Master
Cost: 2 pool
Unique location.
+1 hand size. Minions you control can unlock after resolution of a successful action to equip with a non-electronic, non-vehicle, non-weapon equipment card from your hand; a minion can unlock only once this way each turn. {Non-electronic, non-vehicle, non-weapon} equipment cards cost minions you control -1 blood or pool to equip.

Name: Catacombs
Cardtype: Equipment
Cost: 1 blood
This equipment card represents a location and does not count as equipment while in play. Unique.
When attempting to rescue a vampire from torpor, the vampire with this location gets +1 stealth and burns 1 less blood if successful.

Name: Therbold Realty
Cardtype: Master
Master: unique location.
Locations cost you 1 less blood or pool.

Name: Pier 13, Port of Baltimore
Cardtype: Equipment
Cost: 2 blood
This equipment card represents a location and does not count as equipment while in play. Unique.
During your influence phase, this minion may equip with a non-location, non-unique equipment card from your hand (requirements and cost apply as normal). This is not an action and cannot be blocked.

Yes. See also allies that are able to recruit other blood-costing allies whose blood cost has been reduced to 0, cf. rulings around The Shard, London.