In a perfect world, I'd have each player own a copy of the book. When spending xp and knowing what's next, passing around 1 book can take quite a lot longer than needed when having to pass the book around. Especially if a player wants to purchase a new Specialization and wants to see which Specialization fits with the background of the character.
In reality, I might just print out the Specialization Trees and keep them in a notebook and if a player wants to know about a certain Career's Specializations, they'd just be passed those Specializations.