coPuppe sequence for a cofiber sequence

Lemma 2.4.28 (coPuppe sequence). Given a cofiber sequence \(X \xrightarrow {f} Y \xrightarrow {g} Z\) in \(\An _*\), there is a sequence \[ X \xrightarrow {f} Y \xrightarrow {g} Z \xrightarrow {\delta } \Sigma X \xrightarrow {-\Sigma f} \Sigma Y \xrightarrow {-\Sigma g} \Sigma Z \xrightarrow {-\Sigma \delta } \Sigma ^2X \to \dots \] in which every consecutive triple forms a cofiber sequence.