I find the definition of Thom space on the book Characteristic classes, J.W. Milnor, J.D. Stasheff, page 205:
For a vector bundle $\xi$ with a Riemannian metric over a $CW$-complex $B$, let $A$ be the subset of the total space $E(\xi)$ consisting of all vectors $v$ with $|v|\geq 1$. Then the space $E(\xi)/A$ in which $A$ is pinched to a point is called the Thom space of $\xi$, denoted by $T(\xi)$.
Question. Let $B_0$ be a $CW$-subcomplex of $B$ and $\xi_0$ the restriction of $\xi$ on $B_0$. Are there any references for the definition of the relative Thom space of the pair $(\xi,\xi_0)$?