Here's why you might think it does, and what it actually uses instead:
* Rhyme: The poem uses a lot of rhyme, specifically an ABAB rhyme scheme. This might give the impression of alliteration because similar sounds are close together, but it's not the same thing. For example, "walk" and "talk" rhyme, but they don't alliterate because the "w" and "t" sounds are different.
* Assonance: The poem also uses assonance, which is the repetition of vowel sounds. This can be subtle and contribute to a sense of rhythm and flow.
Let me know if you'd like to explore any specific lines from the poem to see how it uses these techniques!