Sappho's poetry echoes the Homeric tradition. The first poem is a good place to start to examine the similarities. Firstly, there is the invocation of the god or goddess. Secondly, there is the portrayal of the goddess Aphrodite. And finally, there is the comparison of love to war at the end of the poem.
The first 10 lines are the invocation of the goddess. Sappho writes this invocation in the formula that we see in the Iliad. An example in the Iliad is in book 5, lines 115-120. Both invocations begin stating the name of the goddess, her relation to the other gods and then continue with "if ever before you" or "if ever in the past you." Following this, the speaker asks for some blessing. In both cases here, the speaker asks for the ability to conquer – one in war, the other in love.
Also, it is interesting to note that Sappho called Aphrodite "Queen" and then proceeds, in lines 7-10, to describe her descent from the heavens as a regal procession. It is beautiful consistency.
In both the Iliad and this poem, Aphrodite is given voice. Even though Sappho, in line 12, is described as smiling, her following words seem wearied, particularly when she says, "Who is it this time". In the Iliad, 3.413-417, Aphrodite speaks in anger. Also, in the Odyssey (book 8), Aphrodite is portrayed, though there, she does not speak. These three examples of Aphrodite seem to be consistent with each other. In both the Iliad and the Odyssey, she seems fickle at best. Aphrodite says, in the poem, that the object of Sappho's love will shortly change her mind: "For though she flee, soon she'll be giving. . ." and so on. Aphrodite is portrayed exactly as love is portrayed. Also an excellent consistency.
The last segment (lines 20-22) talks of victory. This appears in the invocation in the Iliad, when Diomedes asks Athene to grant that he may be victorious in battle. This comparison of love to battle is a different aspect than we see in either the Iliad or the Odyssey. In both works, men are fighting for a woman, but this is not what is seen in the poem – it is more of a matter of honor there. For Sappho, love is a fight, but it is for a feeling that no one else sees – not for kleos, more like geras. That she mentions freedom from obsession is curious in that it appears that it is a battle for at least her freedom from the madness of desire.
In at least these aspects, Sappho's poetry has remnants of the Homeric tradition. The formula of invocation Sappho uses to Aphrodite can be seen in multiple places in the Iliad. Aphrodite is portrayed similarly in the poem and in the two works, and her embodiment of love is picturesque. And in the end, love is compared to war. This poem is almost a smaller version of the (very) large Iliad.