I think weapons, armor, items or even beings (ex: Rika) called "NEI" are related to a "project" to destruct Dark Force and PD. NEI-weapons are weapons choosed/made by its special characteristics - they are powerful and/or legendary. This doesn’t invalidate any of the opinions posted here, so I think this idea is fine to me.
Even so... could NEI weapons be the same in PS2 and PS3?
It'd be strange to me if they had included the Nei claw in PS2, seeing as how, Nei, would be gone by the end...
So they might have had a lot of the same weapons and some other one. But I really couldn't know.
It's true that not all NEI-weapons were in Dezo Dungeons (ex: NEI-sword and NEI-claw* from PS4drama). In this case the only missing weapon would be the NEI-bow which nobody is able to use (so it would not make sense to appear, just like the claw didn't appear in PS2). So... let's us imagine that NEI-weapons from PS3 are the same NEI-w from PS2. Who came first? The NEI-weapons from PS2 or the NEI-weapons from PS3?**
If NEI-weapons from PS3 came first then that means someone (like Mieu or Searen) that came from spaceship noah (for instance) could have given that NEI-items to the pre-PSII-Espers take care in order to defeat dark force in PS2. Some of them were guarded in Dezo dungeons (ex: slicer and gun) and some inside esper mansion (sword and claw*). In that case the claw was from Mieu and the gun from Searen... witch were the only heroes that could survive from PS3... and if it was Mieu and Searen who gave the weapons where are they right now? Before speculating about that let's see the other perspective first.
If NEI-weapons came from PS2 and were given to people from AlisaIII I really don't understand how NEI-claw* could be on PS4drama. And even if NEI-claw from PS4drama is not a NEI-claw but the last claw used by nei2nd I can't understand how those NEI-weapons (supposedly created by pre-PS2espers) just needed to became again Nei-weapons (weren't they already Nei weapons?)... Anyway it’s possible they lost it's power/charge during the years but Rolf and his team aboard Alisa III would only have 3 NEI-weapons - Lutz could give the missing 2 (claw and bow) but for what purpose, since nobody can used it? And why now, since they previously had to fought dark force?
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* If that's a real NEI-claw, because it could simply be a regular claw nei2nd used before die. "Nei" word is ambiguous (or maybe not).
** The question only works if we assume that Aron's ending really happened and alisaiii spaceship "helped" earthman to find algol.
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Ok, so the only plausible explanation (besides that one witch says they simple are different NEI weapons, with no relation at all – witch is pretty fine) is that PS3 “legendary weapons” became “NEI-weapons” and (with that black hole voyage to the past) they eventually were given to espers (the other sages) in pre-PS2 in order to guard them to future Dark Force appearances.
But if Mieu and Searen made it so far... they couldn't simply disappear... unless they went (again) into Alisa III to help... Orakio (again) - in that case Mieu would (somehow) become Miun and Searen would (somehow) be Siren, witch both would have a sad ending... this would become even more sad… / and could lead to a change in the future of Arisa III (well there are 4 possibilities), who knows?
~what was going on in my mind when I wrote this?