Same session variable retrieved in different blocks not stable

Question

I have a module that have three blocks.

Block No 1 sets the session
Block No 2 gets the session
Block No 3 remove the session

Each block is assigned to a different page.

Now, for some reason this is not working well. I spent the last hours understanding where my mistakes are. The problems are:

1. I don't always see the session value on block 2
2. I don't see the markup in block No 3.
3. The session is not removed in block No 3.
4. The block doesn't always get set in block No 1

This is the block code:

Block 1:

namespace Drupal\achva_sso\Plugin\Block;

use Drupal\Core\Block\BlockBase;

/**
 * Class SsoSessionBlock
 * @package Drupal\achva_sso\Plugin\Block
 *
 * @Block(
 *     id = "achva_sso_session_block",
 *     admin_label = @Translation("Example achva sso session block block")
 * )
 */
class SsoSessionBlock extends BlockBase {
    /**
     * {@inheritdoc}
     */
    public function build(){
        $value = time();
        $session = \Drupal::request()->getSession();
        $session->set('name', $value);


        return [
            '#type' => 'markup',
            '#markup' => $this->t('The output of super SsoSessionBlock block.'),
        ];
    }
}

Block 2:

<?php
/**
 * Created by PhpStorm.
 * User: david_s
 * Date: 14-Nov-18
 * Time: 2:07 PM
 */

namespace Drupal\achva_sso\Plugin\Block;

use Drupal\Core\Block\BlockBase;

/**
 * Class SsoSessionBlock
 * @package Drupal\module_hero\Plugin\Block
 *
 * @Block(
 *     id = "achva_see_sso_session_block",
 *     admin_label = @Translation("Example achva see sso session block block")
 * )
 */
class SsoSeeSessionBlock extends BlockBase {
    /**
     * {@inheritdoc}
     */
    public function build(){
//        $session = \Drupal::service('user.private_tempstore')->get('achva_sso');

        $session = \Drupal::request()->getSession();
        $details = $session->get('name');

        return [
            '#type' => 'markup',
            '#markup' => $details,
        ];

//        $request = \Drupal::request();
//        $session = $request->getSession('name');

//        return [
//            '#type' => 'markup',
//            '#markup' => $session,
//        ];
    }
}

Block 3:

<?php
namespace Drupal\achva_sso\Plugin\Block;
use Drupal\Core\Block\BlockBase;

/**
 * Class SsoSessionBlock
 * @package Drupal\achva_sso\Plugin\Block
 *
 * @Block(
 *     id = "achva_delete_sso_session_block",
 *     admin_label = @Translation("Example achva delete sso session block block")
 * )
 */
class SsoSessionDestroyBlock extends BlockBase {
    /**
     * {@inheritdoc}
     */
    public function build(){

        $session = \Drupal::request()->getSession();
        $details = $session->remove('name');
        if($details !== null){
            $a = 'logged in';
        }else{
            $a = 'logged out';
        }



        return [
            '#type' => 'markup',
            '#markup' => '<p id="aa">sss'. $a .'</p> ',
        ];
    }
}

I am totally lost. Any help would be great. Tried to use simple sessions doesn't work well either...