I've always had dogs and none of them breathe oddly ... they all breathe, like most mammals, through their noses or maybe their mouths.
And less facetiously ... thanks for the opportunity to learn something new. pneumothorax in dogs, okay ... and I hope your dog is doing well.
Seriously, mine all do the same thing. Breathe in, breathe out, brea-brea-breathe in, breathe out. There is that occasional two / three step breath. One of my dogs sleeps right beside my bed so he often has a hand laying on / scratching him and I've noticed that odd breathing with him - is it normal, well, all the dogs I've had over many years will do it sometimes --- does that make it normal?? (( I hope so! ))
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“Properly trained, a man can be dog’s best friend.”
Corey Ford .