Few months ago I replaced battery in my Mazdaspeed3. I bought VARTA Blue Dynamic D47 which fits perfectly. Some technical data below.
Article no.: 560 410 054 313 2
Parameters: 12 V / 60 Ah / 540 A
Dimensions: 232x175x225 mm
Battery replacement is not a rocket science, so I did not need guide, but my friend found this, I think you like it ;)

If you have device (PC, Notebook or sth.) with USB and Windows 8 system, and you want to install AccessTUNER Race software for your COBB AccessPORT, the installer may not be able to find your device. This is because there is not appropriate driver installed for AccessPORT. But this is a workaround: you need to install AccessPORT Manager first, and then get a driver from AccessPORT Manager directory. I found a site where this is described step by step with screenshots, here you are:

On the 1st of August 2013 was released a new version (2.1.1.3) of AccessPORT Manager software with new features, and on the 7th of August 2013 was released version 2.1.1.4 with bug fixes.

Version 2.1.1.4:
Release date: 8/7/13

Bug Fixes:
Beta firmware for V3 Accessports will now update properly.

Version 2.1.1.3:
Release date: 8/1/13

COBB introducing a new AccessPORT v3, with larger, full color, higher resolution screen, customizable multi-gauge display and interchangeable faceplates. New AccessPORT is faster and easier to use but with familiar face, so users of previous version should not have problems with use. More hihlights and photos you can find on COBB site.

On 23 of July 2013 was released new version of AccessPORT Manager software.

Version 2.1.1.1:
Release date: 7/23/13
New Features:
Accessport Manager has a new look, including new icon artwork.
Anonymous usage tracking (optional) added to help us make our products better.
Increased functionality with firmware updates for Accessports.
If desired, a firmware update can begin immediately when new firmware is available.
Bug Fixes:
APM now properly detects when software updates cannot be downloaded.

June 26, 2013 was revealed to the world a new face of Mazda 3. Designers scaled the heights and it becomes a very attractive compact, designed with a new Mazda's philosophy: KODO - "Soul of Motion". I like the exterior and interior design, which is entirely consistent. I also like the fact that the new Mazda has already known from BK model round knobs controls of air conditioning and they changed location of the control buttons on the steering wheel, which was surfeit in BL model.

On 30 of April 2013 was released new firmware for AccessPORT with support for 2006 JDM MS Atenza

Firmware Update 1.6.7.0-5709:
Date: 4/30/2013
New Features:

New Vehicle Support:
Added 2006 JDM MS Atenza Support

Source: Changelog from my AccessPORT device

At the end of 2012 I bought a new set of rims for my Mazdaspeed. They were laying in the garage and waiting for spring to replace a set of winter wheels. I would not like to wear summer tires for new rims earlier, because I want to shift tires pressure sensors to new rims and then wear summer tires. So I went to the tire service for replace wheels, and by the way I cleaned brake calipers, replaced valves in the tire pressure sensors, and the old rims commited to the restoration. How do you like my MPS with new set of rims? ;)

COBB is proud to announce the immediate availability of the 2013 USDM MAZDASPEED3 AccessPORT support! In addition to 2013 US models, we’ve also added Mexican and Japanese MAZDASPEED/Axela/MPS ROM support so more people can enjoy the simple plug and play power of the AccessPORT.

On January 3, 2013 was released new firmware for AccessPORT with bug fix for improved boot-up stability

Release Notes History on AP-MAZ-002 AccessPORT

Firmware Update 1.6.7.0-5253:
Date: 1/03/2013

Bug Fixes:
Improved boot-up stability.