Soooo...... with a little help i have found a Julia Kavney b1890 Liverpool MMN Welsh
Patrick Kavanagh 1891 Liverpool MMN Welsh, Bridget Kaveney  1883 Liverpool MMN Welsh, Kevaney 1882 Liverpool MMN Welsh
There is an 1881 marriage for Martin Cavanagh to Mary Walsh, catholic register for the marriage is Martinim Kearny & Mariam Walsh 30/1/1881 Holycross Lancashire.
If this is them then in 1881 he is here
Name:   Martin Caveney
Age:   25
Estimated birth year:   abt 1856
Relationship to Head:   Son in Law
Spouse:   Mary Caveney
Gender:   Male
Where born:   Ireland
Civil Parish:   Liverpool
County/Island:   Lancashire
Country:   England
Street address:   22 Hodson St
Marital Status:   Married
Education:
Employment status:
.
Occupation:   Laborer Dock
Registration district:   Liverpool
Sub registration district:   Dale Street
ED, institution, or vessel:   1
Neighbors:   View others on page
Piece:   3608
Folio:   12
Page Number:   19
Household Members:   
Name   Age
Mick Walsh   38
Bridget Walsh   44
Patrick Walsh   14
John Walsh   11
Michael Walsh   3
Martin Caveney   25
Mary Caveney   17
John Stanton   38
Michael Mugan   32
Note the Hodson street which is the same address as the 1891 reply #11 by Heywood.
What do you think? Could this line up, i honestly have serious doubts that ordering certificates will confirm anything as the name is never the same nor his job!  

   But the burning question is just exactly what is his actual surname???