Why in Multi-Voxel pattern analysis for fMRI data, covariance matrices of two different stimuli are equal?

I am working on fMRI data using multivoxel pattern analysis.

I am interested to classify two different tasks using the structure of covariance matrices of the searchlight (instead of mean response) for two different tasks. So, I have two covariance matrices for one searchlight related to two different tasks with dimension: voxels \times voxels.

My results show that the covariance matrix of the searchlight can not discriminate the task. Now, my questions:

  1. Why the covariance structure does not have significant differences for different tasks (face-scene or different grating degree of stimuli)?
  2. Is there any biological reason here?
  3. Most of the researchers assume similar covariances for different tasks in their mvpa studies. where does this assumption come from?

It should be noted that the covariance structure of two different tasks for neural data (extracellular recording) is significantly different!

Thank you for your responses.