case1

case1.php

<?php

$case1 = '[
  {
    "from":"03/01/2021",
    "to":"03/06/2021"
  },
  {
    "from":"03/10/2021",
    "to":"03/15/2021"
  },
  {
    "from":"03/20/2021",
    "to":"03/25/2021"
  }
]';

$arrDate = json_decode($case1, true);
$parsed_date = [];

foreach ($arrDate as $key => $date) {

    $month = date("M", strtotime($date['from']));

    if(!isset($parsed_date[$key])) {
        $parsed_date[] = $month;
    }

    if(isset($parsed_date[$key])) {

        $from = new DateTime($date['from']);
        $to = new DateTime($date['to']);
        $parsed_date[] =  $from->format('d') .'-'. $to->format('d');

    }
}

var_dump($parsed_date);