The transition from the previous scene, the Parisis visiting the Sopranos, to this scene which starts with a close-up on the cat, is perhaps the most important transition in the entire episode. It lets us, the audience, know that we have just witnessed something relevant to Tony's imminent death.
Walden: Yeah, he does that, sometimes most of the day, just stares at Chrissy's picture.
Paulie: What the f**k?!
Paulie: This f**king animal is history, today! Pick him up.
Walden: You pick him up.
[Paulie goes for a broom. Tony walks in and Paulie pretends to be sweeping.]
Paulie: T, you see this sh*t? Does it all the time, he says.
Tony: Oh yeah?
Paulie: Look at him staring at that dead kid. Gives me the f**king creeps.
Tony: Walden, give us some privacy.
[Walden takes the cat and leaves.]
In this scene we have more of explicit establishment of the link between the cat and death. Furthermore, we have continued development of Paulie's extreme attitude toward the animal. Meanwhile, Tony is preoccupied with other issues and hence not concerned about the cat.
The subsequent dialogue regarding Paulie passing on the opportunity to "skipper" the "Cifaretto crew" is further establishment of Paulie's extreme precaution with respect to death.
Walden taking the cat is symbolic of Walden playing some role in Tony's death.
Scene: Raceway Gas Station
[After exiting the SUV, Walden shoots Phil, once in the head and once in the chest. In the ensuing commotion, the SUV is left unattended while the transmission is still engaged in 'Drive'. As a result, the SUV starts moving forward and soon crushes Phil's head.]
On first viewing, this scene appears to be a somewhat out-of-place, gratuitous bit of gore intended to shock the audience. In reality, it is a pivotal component of the story. The key point here is that the grotesque post-mortem mutilation of Phil's body was an accident. Unfortunately, it is very much in line with the type of mutilation that might be done out of disrespect for Phil - in many ways similar to the way Tony broke Coco's teeth in Episode 84 (The Second Coming). When Butch learns of Phil's fate, he likely will believe the mutilation was done intentionally and this belief will serve as the impetuous for Butch to go back on his word to "back off". Also, this may well be the reason why members of Tony's family are killed in addition to Tony himself despite the common practice of not touching the family.
The fact that Walden was the shooter supports this interpretation. Walden is inadvertently involved in Tony's death and that is why he was seen holding the cat previously.
Scene: Tony and Paulie Talking Outside Satriales
As the two discuss Paulie's extreme precaution in the avoidance of death and Tony's aggravation with it, the conversation again turns to the cat. There is more clear association between the cat and death and more clear illustration of their respective attitudes toward the two subjects. Included within the discussion is a second reference to the cat catching mice - a re-emphasis of the connection between the cat and Rhiannon.
After Tony leaves the scene, we are left with a wide shot in which the cat has entered the scene. The cat, which symbolizes Tony's death, has replaced Tony.
Immediately following the discussion of the cat and how it "catches mice," we next transition to a sequence in which AJ picks up Rhiannon.