As a 3rd year student of Japanese, I don't have all that wide a vocabulary yet, but have noticed that, typically, the following patterns are observable in terms of the word endings for transitive-intransitive verb pairs: 自動詞 and 他動詞 tend have the same "prefix", but end in
-u (自) / -eru (他)
開く・開ける、届く・届ける、進む・進める、続く・続ける、育つ・育てる etc.
-eru (自) / -u (他)
開ける・開く、切れる・切る、解ける・解く、裂ける・裂く、焼ける・焼く etc.
-aru (自) / -eru (他)
下がる・下げる、上がる・上げる、閉まる・閉める、務まる・務める etc.
-iru or -eru (自) / -asu (他)
出る・出す、覚める・覚ます、溶ける・溶かす、動ける・動かす、生きる・生かす etc.
as well as several other patterns
While I learned many of these words while studying, I compiled this list in part from this source, which I can't verify the accuracy of (the page links to a more updated version that doesn't categorize the pairs by their endings).
One snag that I found myself often caught by is that, especially for the u<->eru ending pairs, the first dozen or so that I learned all followed the pattern "transitive looks like potential of intransitive" (unrelated, but same sound change so it is easy enough to remember, if misleading). I imagine that most textbooks or courses would introduce 続く・続ける earlier on than 裂ける・裂く, due to usage frequency and kanji difficulty if nothing else. Encountering the reverse pattern was a bit confusing for me, because my (ill-founded) intuition was completely backwards. Even more specifically, I find it especially confusing that 開く・開ける can be read as あく・あける or ひらく・ひらける, but the two readings are respectively paired as 自他 and 他自.
Does anyone know, etymologically, how the phonology of transitive-intransitive pairs developed, and why u<->eru appears in both directions? I initially thought that I could mostly figure out which was which by intuition and pattern matching, but it seems that that might be impossible to do universally.
