It's not always trivial to decide whether to call a vowel a monophthong, a diphthong, or a triphthong. In the end, the answer usually depends on who's asking, who's answering, and why the question is being asked. It's almost never useful just to ask this question in a vacuum (like asking if some person is white or if a tomato is a vegetable or if time exists).
What is a triphthong? It depends. The Wikipedia article is confusing, because it appears to conflate the notion of a phone (a phonetic unit) with the notion of a phoneme (a phonological unit). The initial definition given implies that a triphthong is a phonetic thing--a given pronunciation of the nucleus of a monosyllable (not that deciding what constitutes a monosyllable is always trivial) that "has three targets". But even within that definition lies a rub: the word target implies some state that is aimed for. It implies that the speaker (or at least the speaker's tongue) is "attempting" to hit three articulatory configurations during the course of the syllable. If we look at the spectrogram of a carefully pronounced rendition of the word hire produced by a British RP speaker, we will likely see that the formants start at one set of values, hit an inflection point, then end on a third set of values. But that same word, produced by the same speaker at a higher speaking rate in the context of continuous speech, may very well be produced with no inflection point--just initial formant values gliding to final formant values--or even just with more or less a single, unchanging set of formant values. Do we say that that speaker's hire contains a triphthong sometimes, a diphthong sometimes, and a monophthong sometimes? We could. But isn't the tongue "aiming" for the same set of targets every time? Or do we only only count targets that are actually "hit"? How do we decide if they are hit?
Another conundrum: What if that speaker's rendition of hire is indistinguishable from her rendition of higher? If you ask the speaker how many syllables each word has, she'll probably tell you that hire has one and higher has two. That might lead us to conclude that the former contains a triphthong while the latter contains a diphthong followed by a monophthong. But if the two sound and look (in spectrograms) identical, does it really make sense to give them two different labels?
I realize I'm not answering your question but rather asking more questions; hopefully it's becoming apparent to you why your question is not a straightforward one to answer.
As for the vowels in Lana's yups, I (as a native speaker of a dialect of American English) hear some of them as containing a single "vowel quality" and others as containing two. As implied in my comment, it would be more standard in English to consider the initial y of the word to be a consonant, and I don't hear the [u] you transcribed in the one instance. As a phonetician, I go back and forth as to whether to call a vowel that clearly glides from one set of values to another a diphthong or just a "gliding" monophthong. Almost no vowels in American English are truly monophthongal all the time--that is, most vowels, when pronounced slowly and carefully, display formants that glide from one set of values at the beginning to a different set of values at the end. This is even true for [a], which Wikipedia calls a monophthong. So where do we draw the line? Do we just arbitrarily impose some threshold in Hertz beyond which formants can no longer be considered steady-state? Unclear.
