diskutil shows Macintosh HD is missing (with Recovery HD occupying the entire space)
Your Recovery HD doesn't occupy your whole 3 TB drive. It's disk1s3 in the diskutil listing with the common size of 650 MB.

Your Logical Volume Family and the Logical Volume vanished though.


To rebuild it start to your Recovery HD or to Internet Recovery Mode, open Terminal and enter diskutil cs list.
Copy the LVGUUID
To recreate the LV enter diskutil cs createVolume LVGUUID type name size  

In your case probably diskutil cs createVolume 7ABC--i_can't_read_the_rest jhfs+ "Macintosh HD" 100%.  
Now reinstall Mac OS X or restore your system with the Time Machine backup.


Update 1: 

Recovery HD doesn't exist anymore - it was deleted by accident. You have to rebuild your Fusion Drive from scratch now:

Preparation:


Detach any external drive (especially your external Time Machine backup drive)
Restart to Internet Recovery Mode by pressing alt cmd R at startup.
The prerequisites are the latest firmware update installed, either ethernet or WLAN (WPA/WPA2) and a router with DHCP activated.
On a 50 Mbps-line it takes about 4 min (presenting a small animated globe) to boot into a recovery netboot image which usually is loaded from an apple/akamai server.

I recommend ethernet because it's more reliable. If you are restricted to WIFI and the boot process fails, just restart your Mac until you succeed booting.

Alternatively you may start from a bootable installer thumb drive (preferably Mavericks or Yosemite) or a thumb drive containing a full system (preferably Mavericks or Yosemite).


Rebuild Fusion Drive


Booted to Internet Recovery Mode open Utilities → Terminal in the menubar and enter:
diskutil cs list to get the CoreStorage listing.  
Copy the Logical Volume Group UUID, it's the first listed in the listing of diskutil cs list.  
Then delete the Logical Volume Group with diskutil cs delete LVGUUID.
In your case: diskutil cs delete 7ABC--i_can't_read_the_rest
Enter exit and quit 'Terminal'
Open 'Disk Utility'. Enter 'Ignore' if you are asked to fix the drives.
Choose your SSD and partition it: 1 Partition Mac OS X Extended (Journaled),
hit the Options button and choose GUID Partiton table and hit OK and Apply.
Please check that the size is ~121 GB  

Example:  


Choose your HDD and partition it: 1 Partition Mac OS X Extended (Journaled),
hit the Options button and choose GUID Partiton table and hit OK and Apply.
Please check that the size is ~3 TB  

Example:  


Quit Disk Utility and open Terminal
Enter diskutil list

Example (your disk identifiers and sizes are different of course: Your volume SSD probably has the Identifier disk0s2 and the size 121 GB and your volume HDD probably has the Identifier disk1s2 and the size 3.0 TB):


Enter diskutil cs create "Name" IdentifierSSD IdentifierHDD
In your case probably diskutil cs create "Macintosh HD" disk0s2 disk1s2.  

Copy the resulting LVGUUID

Example: 


Enter diskutil cs CreateVolume LVGUUID jhfs+ "Macintosh HD" 100%.

Example:


Enter diskutil cs list
Check the size of your Logical Volume. It should have the size ~3.121 TB

Example:


Quit Terminal
Open 'Disk Utility' and check your newly created volume for errors
Quit 'Disk Utility'
Attach your external Time Machine backup drive or check this answer if you use NAS or another network share.
Open 'Restore from Time Machine Backup'
Choose the appropriate Time Machine backup and restore your system
Reboot to your restored system.
Unmount and detach your Time Machine backup drive
Open 'Terminal' and enter 'diskutil list'
Check if your 'Recovery HD' is listed.
If your 'Recovery HD' is missing, usually reinstalling your current system with the latest available system installer (e.g. 'Install OS X Mavericks (10.9.5)' if Mavericks is currently installed) will recreate it without loosing any data. AFAIK Recovery Partition Creator 3.8 will NOT create a Recovery HD on CoreStorage volumes.
After reinstalling the system with the latest available system installer open App Store and install the latest security fixes.