In Guillemin and Pollack's Differential Topology book, they use the notion of transverse, but not the \pitchfork to denote it. It is very similar, but has a 'T' in it instead of just a ' | ' in the symbol.
The following picture (taken from the book preview in Google Books, page 68) shows the symbol
I and my peers have searched for a convenient way to produce this symbol, but the quick and easy ways produce unsatisfying result, such as \overline and \bar. Before we go and draw one and make a command, I thought I would see if anyone has knowledge of this being available in some package or a better way to get what we want. Thanks.