The Handbook of English Pronunciation. (Marnie Reed, John Levis referring to J.C. Wells)
Аs the pronunciation of most speakers is rhotic, there are no centring diphthongs, because the vowels /ɪə, eə, ʊə/ in words such as peer, pair, and poor are a sequence of a monophthong followed by /r/ so the rhyme of these words is /ɪr/, /er/, and /ʊr/ respectively.
Acoustics of American English Speech: A Dynamic Approach (Joseph P. Olive, Alice Greenwood, John Coleman)
There are five diphtongs in American English, /eʲ/ as in bait, /aʲ/ as in bite, /ɔʲ/ as in boy, /aʷ/ as in cow and /oʷ/ as in boat.
Oxford Dictionary marks /ɪə/, /eə/, /ʊə/ as strictly British.
Wikipedia quoting Wells in "General American English" article.
When prosodically salient, the lax vowels /ɪ, ʊ, ɛ, ʌ, æ/ tend to be realized as centering diphthongs [ɪə, ʊə, ɛə, ʌə, æə] instead of the more usual long monophthongs [ɪˑ, ʊˑ, ɛˑ, ʌˑ, æˑ] when they precede a word-final voiced consonant, so that the word good in the sentence that's very good! tends to be pronounced [ɡʊəd] instead of [ɡʊˑd].
That is why fear [fɪr] may become [fɪər] or poor [pʊr] may become [pʊər] when emphasized just as well. In my humble non-native speaker opinion.
Why, despite all that, do I keep seeing guides like this that insist on existence of these diphthongs in AmE? Is it a sort of alternative theory I'm not aware of, or do these authors interpret diaphonemic notation literally?