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I need to merge two or more categories products and filter the common products from the collection.

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Here's one way of doing it.

First, get the products ids from one category:

$productCollection1 = Mage::getResourceModel('catalog/product_collection')
                       ->addCategoryFilter($categoryId1)
                       ->getAllIds();

Then get the products ids from the second category:

$productCollection2 = Mage::getResourceModel('catalog/product_collection')
                       ->addCategoryFilter($categoryId2)
                       ->getAllIds();

Then you can intersect the two arrays of product ids to be sure you get the product ids that are available in both categories:

$finalProductIds = array_intersect($productCollection1, $productCollection2); 

Finally, if you need to get every detail about those products you can create a new collection based on the final array:

$finalProductCollection = Mage::getResourceModel('catalog/product_collection')
                          ->addAttributeToFilter('entity_id', array('in' => $finalProductIds));

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