Let $M^n$ be a differentiable manifold and $\pi\colon E\to M$ is $n$-dimensional vector bundle over $M$.
We have a zero section $s\colon M\to E$ of $\pi$.
How can I make a section $s'$ which is trnasversal to $s$? (i.e., $s'$ vanishes $s$ finitely many times.)
(In some text, it seems even possible to make $s$ and $s'$ are isotopic.)
I need this to interpret the euler class of $\pi$, $\chi(\pi)$ as an algebraic intersection number of $s$ and $s'$.
Are there anybody who can give me any references?