Why does Eren loses his equipment after being Titan ? And why Annie doesn't lose the equipment after being Titan ?
That old bearded titan who ate Eren didn't take a bite of him, he swallowed Eren. so Eren will be dissolved in his stomach's acid, but Eren unconsciously activated his titan power and turned into a titan and.... so his ODM gear slings must have been torn apart while he was inside the titan's belly.
Ook, so in anime, he still have a gear when being eaten.
In the scene inside "Santa's" belly we dont see if Eren has it, but there's no reason he would loose it. The gear is very reliable and you won't loose it even while doing crazy acrobatics in mid of an air. He also has his jacket. He transforms and he still has his jacket.
We see him in human form when he emerge from his titan body - He doesnt have a jacket or gear with him. This shouldnt be a case, since in season 3 Eren emerges from his titan body still with a gear. Like you mentioned, other titan shifters also keep their gears (Reinar, Annie, Bertholdt).
So I checked the manga and it's the same thing - Eren is missing his gear and jacket after emerging although he transformed wearing it. I don't think there's a reason to that - it seems ity's just an incositancy carried from manga to the anime.
There's no reason to assume it was damaged inside the Santa's belly or after Eren's transformation - since it's never happened again Also someone was suggesting the gear melted inside the belly... well, we see bodies inside the belly none are damaged by temperature, so it wasnt hot enaugh for gear to melt. Also like i mantioned, the gear is super solid, it can't just break, it has too sustain a lot of pressure during the acrobatics - so i dont think eren would just loose it.
Titans do not lose their equipment when they transform. The only reason Eren lost the gear once in S1 is because he had been partially eaten, sitting in another titans stomach. Showing him without clothes is more of a creative choice implying that before he changed, he was so damaged that he didn't have clothes/gear still attached to him.
Well it wasn't explained so it's probably just a mistake in the animation.The only other reason could be it melted but, that would make no sence at all because, he was wearing clothing still.The reason i said it melting was because one of his titans abilities lights it's self on fire.Meaning it's body temperature rises until it lights on fire.But even so his clothes would have burned off if that was the reason.So it must be a minor mistake that was overlooked.