Note that word2vec is not inherently a method for modeling sentences, only words. So there's no single, official way to use word2vec to represent sentences.
Once quick & crude approach is to create a vector for a sentence (or other multi-word text) by averaging all the word-vectors together. It's fast, it's better-than-nothing, and does ok on some simple (broadly-topical) tasks - but isn't going to capture the full meaning of a text very well, especially any meaning which is dependent on grammar, polysemy, or sophisticated contextual hints.
Still, you could use it to get a fixed-size vector per short text, and calculate pairwise similarities/distances between those vectors, and feed the results into dimensionality-reduction algorithms for visualization or other purposes.
Other algorithms actually create vectors for longer texts. A shallow algorithm very closely related to word2vec is 'paragraph vectors', available in Gensim as the Doc2Vec class. But it's still not very sophisticated, and still not grammar-aware. A number of deeper-network text models like BERT, ELMo, & others may be possibilities.
Word2vec & related algorithms are very data-hungry: all of their beneficial qualities arise from the tug-of-war between many varied usage examples for the same word. So if you have a toy-sized dataset, you won't get a set of vectors with useful interrelationships.
But also, rare words in your larger dataset won't get good vectors. It is typical in training to discard, as if they weren't even there, words that appear below some min_count frequency - because not only would their vectors be poor, from just one or a few idiosyncratic sample uses, but because there are many such underrepresented words in total, keeping them around tends to make other word-vectors worse, too. They're noise.
So, your proposed idea of taking individual instances of travel & replacing them with single-appearance tokens is note very likely to give interesting results. Lowering your min_count to 1 will get you vectors for each variant - but they'll be of far worse (& more-random) quality than your other word-vectors, having receiving comparatively little training attention compared to other words, and each being fully influenced by just their few surrounding words (rather than the entire range of all surrounding contexts that could all help contribute to the useful positioning of a unified travel token).
(You might be able to offset these problems, a little, by (1) retaining the original version of the sentence, so you still get a travel vector; (2) repeating your token-mangled sentences several times, & shuffling them to appear throughout the corpus, to somewhat simulate more real occurrences of your synthetic contexts. But without real variety, most of the problems of such single-context vectors will remain.)
Another possible way to compare travel_sent_A, travel_sent_B, etc would be to ignore the exact vector for travel or travel_sent_X entirely, but instead compile a summary vector for the word's surrounding N words. For example if you have 100 examples of the word travel, create 100 vectors that are each of the N words around travel. These vectors might show some vague clusters/neighborhoods, especially in the case of a word with very-different alternate meanings. (Some research adapting word2vec to account for polysemy uses this sort of context vector approach to influence/choose among alternate word-senses.)
You might also find this research on modeling words as drawing from alternate 'atoms' of discourse interesting: Linear algebraic structure of word meanings
To the extent you have short headline-like texts, and only word-vectors (without the data or algorithms to do deeper modeling), you may also want to look into the "Word Mover's Distance" calculation for comparing texts. Rather than reducing a single text to a single vector, it models it as a "bag of word-vectors". Then, it defines a distance as a cost-to-transform one bag to another bag. (More similar words are easier to transform into each other than less-similar words, so expressions that are very similar, with just a few synonyms replaced, report as quite close.)
It can be quite expensive to calculate on longer texts, but may work well for short phrases and small sets of headlines/tweets/etc. It's available on the Gensim KeyedVector classes as wmdistance(). An example of the kinds of correlations it may be useful in discovering is in this article: Navigating themes in restaurant reviews with Word Mover’s Distance