... are exact. To prove this, we follow Puppe's method. Lemma 3 .
In the case of the method of killing homotopy groups, you have no idea how far you can get before you run up against some ambiguity and don't know how to settle it. In the case of the spectral sequence, the situation is clearer: the groups Ext~'t (H*(Y), H* (x) ) are recursively computable up to any given dimension; what is left to one's intelligence is finding the differentials in the spectral sequence, and the group extensions at the end of it. This account would be perfectly satisfying to a mathematical logician: an algorithm is given for computing Ext~'t(H*(Y), H*(X)); none is given for computing dr.
An introduction to the theory of canonical matrices by H. W. Turnbull