The hostile-takeover battle between Bermuda reinsurance rivals Endurance Specialty Holdings Ltd. and Aspen Insurance Holdings Ltd. continued unabated this week with no end in sight.

Endurance initially made its pitch to by Aspen in April and upped its offer in June to about $3.2 billion. Aspen has fought back hard, with multiple board rejections of the proposal and letters to shareholders urging them to turn away from Endurance’s increasingly aggressive moves. Endurance, in turn, has written those same shareholders in an attempt to sway them into selling.

Both sides are focusing now on following through with their respective strategies. Endurance announced on July 1 that the U.S. Securities and Exchange Commission declared Endurance’s registration statement relating to its exchange offer to acquire all Aspen common shares as “effective.” The offer allows Aspen shareholders to seek all cash, a mix of cash and Endurance shares or all Endurance common shares if they agree to sell.

Endurance noted in its release that it has also released an updated investor presentation that highlights “the strategic rationale and compelling value” of its proposal, what it is doing to expedite an M&A deal, and how Aspen has endured “historical underperformance” under its current leadership.

Aspen, in turn, is wasting no time in continuing the back-and-forth. The company disclosed on July 1 that it has mailed a second letter to shareholders urging them to sign, date and return a blue revocation card (also included in the package) that would formally reject Endurance’s M&A proposals.

“Do not be misled by Endurance’s claims,” Aspen writes in this latest shareholder letter. “These proposals are desperate legal practices designed to coerce you into selling your shares at the lowest possible price. Aspen strongly urges shareholders not to sign any white authorization cards sent to you by Endurance.”

In other words, the battle continues.