Is it [mɛən] or [mæən] ?
I've seen both of them in some videos; however, I'm not really sure Which one of them truly represents the sound (with the æ raising).
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There are three issues here, one about the sounds themselves and two about the conventions of transcriptions. /mæn/ etc. implies either "underlying form" or "phonemic form", which are completely different things – the notation is used indiscriminately. The difference between underlying forms and phonemic forms is a technical distinction that you probably don't care about. [mæn] etc. says "this is how it is pronounced", which also can be the same as the phonemic form.
The issue about the sounds themselves is, who's talking? The vowel in "man" varies substantially, depending on dialect. Either [æ] or [ɛ] is reasonable. The second issue about conventions is that the cardinal vowel standard for how [ɛ] and [æ] are pronounced is, well, a dying art. The vowel usually written æ in English is not the same as either ɛ or æ as observed in the Jones-Ladefoged-Esling-Wells-House performances, and people typically select the "nearest vowel" from the defined set of vowels. People differ in their judgements of closeness.
All that said, the majority of people transcribe man as [mæn], then [mæən] is a distinct minority transcription. Writing [mɛən] is hardest to defend, since "men" is pronounced different (unless it isn't in that dialect), and without the use of diacritics, there is no reasonable distinct transcription of men possible if you think man is [mɛən]. Unless you transcribe men as [mɪən], which is how it sounds in some dialects. So you have to check the author's theory of transcription and the dialect they are talking about.