In his essay on Deep Red, Aaron Smuts proposes a Humean “principle of association” operating within the film, intensifying the visceral impact of its murder set-pieces amongst other things. By this he means the way in which Argento and his co-writer Bernardino Zapponi try to associate the film's horrors within everyday experiences that the viewer is likely to have had and then intensify or amplify them to operatic proportions.
Another type of association is found within Deep Red's own diegesis, as events and pieces of dialogue foreshadow the later murders: Marc's pseudo-Freudian interpretation of how when playing the piano he is “really” bashing bashing his father's teeth thus associate with Professor Giordani's having his teeth smashed against the fireplace by the killer; Marc's being blasted with steam by an espresso machine (“hey”) with Amanda Righetti's having her head immersed in boiling water, and so on.
It is an idea that also seems to have considerable mileage in relation to the internal logic of Inferno in particular. I am not just thinking of the way in which Sara cuts her hand on the taxi door and Rose hers on a broken doorknob prior to their murders, on the same night, one in Rome and the other in New York, but also some of the otherwise inexplicable inserts that Argento includes.
In time but not place?
New York, the very same night...
Might the perplexing shots of black-gloved hands snipping the heads off paper dolls refer to Rose's guillotining with a window pane in particular (if you look carefully a statue of Napoleon can be seen in the window of Kazanian's antique shop, among the more usual giallo/surrealist dolls; while the guillotine also appears more obviously in Trauma) and the lizard eating the butterfly to the stuffed animals that she finds in what appears to be a deserted and dilapidated version of the alchemical laboratory Sara discovers in the library in Rome?
There is no definitive answer, of course, but that is the whole point and why the film so frustrates when approached with a conventional meaning seeking and fixing mindset.
“There are more things in heaven and earth [...] than are dreamt of in your philosophy” and, indeed, to the Argento text, where "beauty will be convulsive or not at all"