homotopy for maps of pairs of spaces

Let \((X,A), (Y,B)\) be pair of spaces and \(f,g: (X,A) \rightarrow (Y,B)\) map of pairs. Then a homotopy from \(f\) to \(g\) is a homotopy

\begin{align*} H: X \times [0,1] \rightarrow& Y \end{align*}

from \(f\) to \(g\) such that

\begin{align*} H[ A \times [0,1]] \subseteq B \end{align*}

i.e. \(H\) restricts to a homotopy from \(g_{\vert A}\) to \(f_{\vert A}\) on

\begin{align*} H: A \times [0,1] \rightarrow& B \\ \end{align*}