How was it possible to summon Sasori with Edo Tensei? As we know, Sasori has 


   turned his body into a puppet, with a small "core of living flesh" being the only living part of it: 


This question also states that when summoned by Edo Tensei, 


  the reincarnated seem to retain any permanent body damage and physical
  limitations they received during their lifetime.


Obviously, Sasori would fall under someone who had suffered some physical...limitations. We know that 


   after being brought back by Edo Tensei, Sasori eventually was released, and vanished like any other summoned shinobi (of flesh and bones), so it clearly wasn't another puppet: 


So how was Kabuto able to summon Sasori? If the reincarnation retains body damage, wouldn't he only be able to reincarnate Sasori's "Living Core"? I doubt that the process of "enchanting", which Kabuto can perform, involves re-making the whole body.
Although the Wiki does says that  


  the reincarnated seem to retain any permanent body damage and physical limitations they received during their lifetime1  


it also says that  


  Kabuto can also modify his summoned fighters (...). While the technique usually reincarnates the deceased at the exact state they were in at the time of their deaths, Kabuto noted that he brought Madara back in a state that was "beyond his prime" and was reincarnated much younger than when he died an old man as well as instilling him with abilities he had acquired in his old age.


The best explanation (I can come up with) for this is that he was reincarnated into an earlier body, maintaining the abilities and memories acquired until the time of his death, much like Madara's reincarnation 2. Although I don't think he needs to re-make the bodies of the summoned, if it meant that, it was already proven that he could do it (it was made with Madara), so it would also be possible to make it with Sasori.  



1 This piece of data is stated in the Wiki, but I do not recall if it was referenced in any manga chapter, so bear that in mind.
2 Naruto chapter 560, page 3. Kabuto explains Madara that he brought him beyond his prime.