LibreOffice will do this. Being familiar with MS Word the method would not
be what is expected.
Four page styles need to be used for the scenario as you've describe.
page 1: a "front cover" page style
page 2: a blank page style
page 3: an "ODD pages" style
page 4: an "EVEN pages" style
I believe, based on the description of front cover and page 2 the same
could be accomplished with only three page styles.
page 1 & 2: the default page style (this includes headers and footers but
if they aren't used their presence shouldn't matter)
page 3: an "ODD pages" style
page 4: an "EVEN pages" style
Writer has several included page styles that should support this
requirement. They are "Default Style", "Left Page", and "Right Page".
Create the cover. It will be using the Default Style page style.
With the cursor at the last element on the cover page (use the keystroke
Ctrl+End to be sure you're at the last part of the cover page)...
Select from the menu "Insert | Manual Break...",
Select the "Page break" option and for Style select "Default". Click the OK
button.
The cursor should now be on the 2nd page.
Press enter once (I don't know why this is needed but it is the only way I
could make it work).
Insert another page break via the menu. This time set the Style to "Right
Page". The cursor will be at the top of the 3rd page.
The third page of the document will have the "Right Page" format. As
content is entered and it fills this page and goes onto the next the next
page will automatically have the "Left Page" format applied.
These instructions were composed with reference to LibreOffice 4.2.6.2 on
Ubuntu 10.04.