Long exact sequence of a Serre fibration

Theorem 2.3.14 (Long exact sequence of homotopy groups, Switzer (1975), Theorem 2.59). Let \(p\colon E \to B\) be a Serre fibration and consider a point \(e \in E\) with image \(b := p(e)\). Define the fiber \(F_b\) as the following (strict) pullback of topological spaces:

Then there is a long exact sequence of homotopy groups of the form \[ \dots \to \pi _{n+1}(B,b) \to \pi _n(F_b,e) \xrightarrow {i_*} \pi _n(E,e) \xrightarrow {p_*} \pi _n(B,b) \to \pi _{n-1}(F_b,e) \to \dots \]