How does the narrator convince you that he has become an axolotl?

In Julio Cortazar's short story, "Axolotl," the narrator becomes obsessed with the Mexican salamander, axolotl, after he visits the Jardin des Plantes, in Paris. At first, he is only fascinated by it, almost entranced by its features. This is illustrated in the first three paragraphs in which the narrator describes the anatomy of the axolotl.
In the fourth paragraph, the narrator begins to identify himself with, or as, the salamander by speaking in the first-person from the perspective of the creature. This is emphasized when the narrator, still speaking as the salamander, begins to describe the living conditions inside the aquarium.
By this point in the story, the narrator is gradually metamorphosing into the axolotl. In the final paragraphs, we learn that the narrator fully transforms into the axolotl, but he sees his original human face reflecting from the glass. The author uses shifting perspectives to guide the reader through the transformation.