I know extremely little about the history of sound changes in languages other than English, so that will be the source of my examples. However, I’m asking this question for a more general, cross-linguistic context.
Mentally going through the variety of phonological/phonetic vowel mergers which have occurred in various accents of English, it’s clear that many have been related to the presence of certain consonants.
Some have happened next to the liquid phonemes /l/ and /r/. For example, the MERRY-MARY-MARRY, HURRY-FURRY, FUR-FIR-FERN, CHEER-CHAIR, SQUARE-NURSE, and SIRIUS-SERIOUS mergers precede historic /r/, and the FOOL-FULL, FOOL-FALL (not sure if that's an established term), FILL-FEEL, and HULL-HALL mergers precede historic /l/. Admittedly, some of those may have occurred after the liquids were already vocalized or dropped.
Others occur near nasals. PIN-PEN is very well known, and the weak vowel merger seems especially strong before /n/ as in the keywords chicken and thicken. I think some California speakers have something like a MORPHING-MORPHINE merger. In my accent (GenAm with mild Inland North features), the vowels in "strength" and "thank" sound almost exactly the same as the vowel in "pain," and I find it baffling that most transcriptions for American English show all three as different.
It seems like there must be something special about liquids and nasals that facilitates the spread of vowel mergers. Both are among the more sonorant consonants in English, but I'm not aware of any mergers around /w/ or /j/ (unless you count yod-dropping and coalescence as vowel mergers), which are the most sonorous of all, or /m/, another nasal.
Can a rough hierarchy of sounds likely to facilitate mergers in their phonological environment be produced? Alternatively, are there any distinct criteria that might indicate the likeliness of mergers near a certain phoneme? Examples of mergers in other languages would be helpful.
Please note that I’m NOT asking about what type of sounds are likely to become merged, which is more obvious. Rather, I’m asking about the phones that facilitate mergers for other sounds around them.