Liddle, 29, made 61 league appearances for the Bantams and has joined for an undisclosed fee.
Dimaio, 20, was a free agent after being released by the Blades after making five appearances for the club.
Anderson, 22, who is yet to make his Clarets debut, has joined on loan until the end of the season.
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Chesterfield have signed Bradford City midfielder Gary Liddle, ex-Sheffield United midfielder Connor Dimaio and Burnley defender Tom Anderson.