  It was proved by Fan--Lee and Fan that the absolute Gromov--Witten invariants
of two projective bundles $\mathbb P(V_i)\rightarrow X$ are identified
canonically when the total Chern classes $c(V_1)=c(V_2)$ for two bundles $V_1$
and $V_2$ over a smooth projective variety $X$. In this note we show that for
the two projective completions $\mathbb P(V_i\oplus\mathcal O)$ of $V_i$ and
their infinity divisors $\mathbb P(V_i)$, the relative Gromov--Witten
invariants of $(\mathbb P(V_i\oplus\mathcal O),\mathbb P(V_i))$ are identified
canonically when $c(V_1)=c(V_2)$.
