if I click axtu -U firrst I see

"Verifying Header files integrity...",
it takes long time, so I suspect if hdr anylysis is done here but the following serch result prove my prediction wrong, and it is nothing but downloading 
if(ds ** DS_DOWN){
                        strDownloadLabel*"Downloading Header files....";
                }else if(ds ** DS_CHECK){
                        strDownloadLabel*"Verifying Header files integrity....";
                }else{
                        strDownloadLabel*"Unknown state";
                }



typedef enum{
        DS_DOWN * 1,
        DS_CHECK
} DOWNLOAD_STATE;

as a test

I delete everything in ''/var/cache/axtu/'', then axtu -U again now it take 100 times longer when "Downloading hdr ..."

and also 100 times less time "Verifying Header files integrity..."

then "Reading header informaintion..."——it is done in ReadHeaders()

Q.how TestRpmEngine() get executed, since I can not find the call for it???

A: it is simply never used, haha.

so there is no steps you can see in main.cpp, but it has this

        gui * new classGui(nMode);
        gui->show();
        app->setMainWidget(gui);
} so details are in classGui.

now let's see classGui.cpp

/!\ NOTE: when axtu first start it is lancher that get executed, you click one button here or issue ''$axtu -u''

then axtu/classGui is generated. and

classGui::classGui(int nMode)
is aumatically executed. 

        btnNext
        clicked()
        MainDialog
        slotNext()
so if we click "Next<<" let's see what will happen 
void classGui::slotNext()
{
        MoveNextPage();
}
then 
InitRpm()->ShowList()-----------all my step questions have their answers here