"Anniversary" doesn't use rhyme or a steady meter, but it's still a very lyrical poem. This is in large part thanks to consonance (and, sometimes, alliteration), which make the poem's language sound more intense, musical, and memorable.
In stanza 1, for example, /f/ alliteration highlights the image of the speaker's mother surrounded by "feathers of flame." Those fricative sounds might also evoke the flickering of a flame itself. Later, soft /s/ and lilting /l/ sounds make the image of the afterlife more reassuring. There's something hushed and comforting about the sounds of this passage:
In the perpetual Sunday Morning
Of everlasting, they are strolling together
Listening to the larks
In this way, the poem's sounds often enhance its imagery. For another example, listen to the pounding /d/ alliteration and consonance of line 17:
Down a deep gorge of woodland echoes:
These sounds evoke the power of Hughes's mother's "piping" voice as it "echoes" through the afterlife.
Hughes also uses consonance to control the emotional register of the poem. In lines 25-30, for example, sibilance (as well /f/, /th/, and /sh/ sounds, which are often considered sibilant in their own right) illustrates his mother's anger and grief as well as his own sadness. Speaking about himself in the voice of his mother, he writes:
Are the mass marriages of him and his brother
Where I was not once a guest." Then suddenly
She is scattering the red coals with her fingers
To find where I had fallen
For the third time. She laughs
Helplessly till she weeps [...]
All these hissing, slippery, hushed sounds evoke both bitter anger and deep sadness.