Let me start by saying this is my first post. I am new to intersection theory and am currently reading Guillemin and Pollack's Differential Topology and have a question on the intersection of $3$ curves in $\mathbb{R}^3$
Let us say we have $3$ curves in $\mathbb{R}^3$, for example, the $ x$, $y$, and $z$-axis. I think they satisfy the transversal intersection property because their tangents span all of $\mathbb{R}^3$ but intuitively it doesn't seem to be a stable intersection (I could just slightly move one of the curves away from the others and the intersection would be removed). Is this specific example an example of a transversal intersection in $\mathbb{R}^3$? I would also like to orient this intersection and would like some input on that. Would something similar to the scalar triple product be of use to me?
Anything that can help me resolve this or any references that I should read further to help clear this up is appreciated