RobV15, my initial thought was, well, I couldn't understand your diagram at all.
Maybe for your description you could write a clear point form of what exactly you are wanting this transfer contraption to do.
For example, what power level are you talking about, a power board on a cord or the main house panel, are you talking tens of Watts or tens of Kilo Watts?
I would suggest you look at using a two stage control from Arduino digital output to first small relay to control the main AC contactor.
I don't see that you can get a mechanical relay that can be controlled from a small control signal such as from an Arduino and have it pulling in a large contactor.
Have you looked at using SSR, Solid State Relays, they are easy to use and can be driven directly from a logic output such as from your Arduino.
As mentioned, if you use mechanical relays, use flyback diodes across the coil of any DC relay and for any AC contactor, use a snubber (RC) circuit.
as for the relays, I will be getting the relay boards that come with the diodes and transistors
Which board is that, provide a link?
And what ever board that is, is it designed and rated for use with your 120Vac mains supply system?
You will provide the required barrier isolation between your Arduino and mains potential?
Instead of using a battery, look into 'supercaps', if you are only needing to keep the control circuit alive for tens of milliseconds.
Also, describe clearly how you want to process to happen, in terms of when mains power is lost to when mains power returns.
I can only guess you are trying to emulate what a typical offline UPS does in the event of power loss?
I just noticed another post by you in the 'Home Automation & Networked Objects' section, http://arduino.cc/forum/index.php/topic,147249.0.html
From the photo it seems you know about solide state relays (SSR) I mentioned above.
The wiring looks to be neatly done in the enclosure, but I am concerned that it looks to be a metal box and just wondering if you have it earthed for safety?
Please tell me you understand the risks and have knowledge with working with mains power systems?
Also, is that the same type of relay board you are wanting to use in this project?