"Closely mimics" is precisely right. I think Guadagnino promotes a sisterhood between Emma and the identity-shifting character played by Kim Novak in Vertigo. These are women in the process of transformation; they are remaking themselves. Sometimes I feel Guadagnino underlines the connection between the characters a little too strongly. Guadagnino is quoting directly from the Master by having Emma wear her hair tied in a bun in the back with a curl at the end; the camera tracking behind, directing our gaze to the back of Swinton's head just like in Vertigo.