Firing Up A New Tank With Old Tank Media

[manofish123]

Getting 0-0-80 readings on a new tank fishless cycle now for 4 days and getting ready to do a 80-90% water change prior to adding my fish. My question is : I have an intake tube sponge in this old tank as well as a filter sponge, white tablet pack and the carbon pack that I assume all have bactria on them now.
I'm wondering if when I make this water change on the old tank, could I put this old water and intake sponge in the new tank to assist in cycling ? The cycled tank is a 6 and the new one a 10 so I would have to add at least 4 gallons of conditioned tap water to the 10. Just wondering if this is a good idea or should I just pitch the old water and start from scratch ? Also if I "can" use the old intake sponge as a starter in the new tank, will it reduce the bacteria in the old tank substantially ?
Thanks for any and all help ...