With/Having/ his attention grabbed

Many times, I see three different ways in expressing the details of the sentence. 1) absolute phrases with past participles, 2) Prepositional Phrases, and 3) Participial Phrases. I wonder if they are semantically equivalent and if any one is more idiomatically more favorable to the others.

Example:

• His attention grabbed, John turned to Sera.
• With his attention grabbed, John turned to Sera.
• Having his attention grabbed, John turned to Sera.