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Hello. My name is Alex.Thank you for your question.I will be happy to provide you with information you are seeking for educational purposes only.
What actual evidence / proof do you have the the bedbugs infestation was caused by the neighbors?
Thank you for your follow up.
The Landlord is generally responsible for the cost of extermination of any pest, including bedbugs.
Did the tenant give you written notice of the bedbug issue, before contacting and hiring an exterminator, so you would have a chance to hire an exterminator of your own choice?