There can be only one copy of the tool at a time. The resurrected shinobi get their tools if they have not been acquired by others in the real world.
When the Seven legendary swordsmen were summoned, initially only Zabuza had his Kubikiribōchō. Although Suigetsu had acquired it, it was taken away from him when he was arrested at the five Kage meeting. Thus, it seems the Edo Tensei transferred it to Zabuza.
Later, Mangetsu summons 4 other swords from his scroll. He had presumably sealed them in his scroll before he died, which is probably why they were not acquired by others.
The only swords missing are the Samehada and Hiramekarei, which were in possession of Bee and Chojuro respectively. Similarly, Sasori did not get his puppets, because Kankuro had taken their possession.