My H-1B transfer is pending — can I start working at the new company?

Question

I've been on an H-1B with my current employer for 3 years. A new company filed a transfer petition for me 2 weeks ago and I have the receipt notice. My new manager wants me to start Monday, but my current employer says I can't leave until the transfer is approved. Who is right? I don't want to do anything that puts my status at risk.