Long exact sequence of homotopy groups of spectra

Proposition 4.4.30 (Long exact sequence of homotopy groups). Let \(X \xrightarrow {f} Y \xrightarrow {g} Z\) be an exact sequence of spectra. Then there is a long exact sequence of homotopy groups of the form \[ \dots \xrightarrow {} \pi _{1}(Y) \xrightarrow {g_*} \pi _{1}(Z) \to \pi _0(X) \xrightarrow {f_*} \pi _0(Y) \xrightarrow {g_*} \pi _0(Z) \to \pi _{-1}(X) \xrightarrow {f_*} \pi _{-1}(Y) \xrightarrow {} \dots . \]