Mazda 6 Service Manual: No.13 no kickdown

No.12 torque converter clutch (tcc) non-operation

No.14 engine flares up or slips when upshifting or downshifting

Other materials:

Mazda 6 Service Manual: Traction Control System (TCS)
The Traction Control System (TCS) enhances traction and safety by controlling engine torque and braking. When the TCS detects driving wheel slippage, it lowers engine torque and operates the brakes to prevent loss of traction. This means that on a slick surface, the engine adjusts automatically ...

Mazda 6 Service Manual: Intermittent concern troubleshooting
  Vibration Method 1. If malfunction occurs or becomes worse while driving on a rough road or when engine is vibrating, perform the steps below. Note There are several reasons vehicle or engine vibration could cause an electrical malfunction. Some of the things to check for are: ...