After losing his first saber in the duel against Darth Maul on Naboo, Obi-Wan built his second saber in his early days as a Jedi Knight. He kept the design. Only small differences can be seen: the boxes on the pommel no longer have holes, and a screw on the emitter no longer has a purple insert.
This lightsaber accompanied him while he trained young Anakin and was taken from him during the mission on Geonosis. During the Battle of Geonosis, Obi-Wan then gets a borrowed lightsaber from Sephjet Josall.
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Behind the Scenes
The lightsaber design was carried over from TPM. It might even still be the same prop, but a newly built version is more likely. Details like the missing holes on the pommel may have been lost through resin casts of the original. Since the AOTC lightsabers look more chrome, the hilt was polished up.
