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Свозил is perfective.
Отвёз also is perfective.

"I took the cat" - it's is imperfective in english and in russian.
I took the cat to the vet - я возил (вчера, год назад) кошку к ветеринару.
If...

Свозил=отвёз, they are synonyms in some cases. I can say "Я отвёз кошку к ветеринару" and keep in mind that I have taken it back. It depends on the context.
Я отвёз кошку к ветеринару и там мне...

If you went by a car - я вёз кошку к ветеринару If you mean a complete action, then: я отвёз кошку к ветеринару.
If you walked without a car - я (от)нёс кошку к ветеринару
If you say just 'I took...