Before revision:  By combining Tikhonov--Fenichel small parameter with scaling analysis  , we derive improved upper bounds on the  error for the sQSSA, rQSSA and tQSSA.
After revision:  By combining Tikhonov--Fenichel small parameter with scaling analysis and energy methods , we derive improved upper bounds on the error for the sQSSA, rQSSA and tQSSA.