How to pronounce 繁栄 han'ei? Is there a glottal stop between the two syllables? Is it //haɴʔeː//, //haɴeː//, //haŋʔeː// or //haŋeː//?
繁栄 and 反映, 半影, ... are pronounced //haɴeː// without glottal stop and ん as //ɴ//.
The combination //ɴ// + vowel is difficult to pronounce, so in some cases, such as 反応【はんのう】, orthography has been adapted to allow for easier pronunciation (although はんおう might still be considered a valid pronunciation). Usually though a word has only a single valid spelling, which sometimes may help to distinguish homophones, e.g. 漢音【かんおん】 and 観音【かんのん】.
This phenomenon is called 連声【れんじょう】 and usually occurs with //ɴ// + //aou//, although the Wikipedia page also gives examples for んゑ > ね.
I guess one should also mention that in the case of //ɴ// + //i//, there is 雰囲気【ふんいき】, which is more often than not pronounced ふいんき...
In any case, //ɴ// + //aiueo// sometimes calls for attention to detail, but putting exceptions aside, ん + あいうえお is pronounced //ɴ// + //aiueo//. In the case of //ɴe// the phonetic realization usually exhibits some palatalization as in [[haɴʲe:]] or nasalization as in [[hãːeː]] (see comments below).