1. Each woman is carrying her own bag.
2. Each woman has her own bag.
3. Each woman is moving her own back (to a place).
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Does #1 mean #2 or #3?
The expression 'is carrying' represent 'the state.' Am I right? Action of State?
"is carrying" is the action the subject is taking.
1 and 2 are common phrasings. I've never heard 3, unless you're referring to moving the bag from one place to another, not just carrying it with her (onto a plane or into a car or ??).