If you want to know which transitions were detected in a spectral library, one way to do this would be to tell Skyline to add all of the peptides to your document and then see which transitions Skyline gives you.
That is, you would go to:
View > Spectral Libraries
and then press the "Add All" button in the Spectral Library Explorer
You should make sure that the setting "If a library spectrum is available pick its most intense ions" is checked at "Settings > Transition Settings > Library".
Also, set "Pick X product ions" to a high number so you Skyline will add all of the transitions that it finds to your document.
You tell Skyline which transitions to look for (b, y ions etc) using the filter settings at "Settings > Transition Settings > Filter".
After you have done this, you would use the "Transitions" report in the Document Grid to see what transitions you got.
You can learn more about the Document Grid in the Custom Reports tutorial:
I imagine that there may be much better ways to do this which involve tools designed to look at your specific type of peptide search results. A .blib spectral library does not really contain any information about which transitions were seen. What it does has is a list of m/z and intensity values. Skyline then uses its own knowledge of peptide fragment m/z's to decide which fragments can be seen in that m/z and intensity list.