Does The Metamorphosis seem to deliberately refer to the myth of Arachne?

In my opinion, it does not. The myth of Arachne is an example of jealousy, violence, and a refusal to submit. Minerva is jealous of Arachne, and as a result, she disguises herself, attempting to extract an apology, berate her, and compete with her. In the end, Minerva beats her violently, leading Arachne to take her own life.... after which, she turns her into a spider. The circumstances regarding Arachne and Gregor are similar, but yet, they are very different. What do you think?